{"id":38,"date":"2018-07-20T11:43:34","date_gmt":"2018-07-20T09:43:34","guid":{"rendered":"http:\/\/mathquiz.fr\/?page_id=38"},"modified":"2018-07-24T14:08:51","modified_gmt":"2018-07-24T12:08:51","slug":"convexite-continuite","status":"publish","type":"page","link":"https:\/\/mathquiz.fr\/?page_id=38","title":{"rendered":"Convexit\u00e9 \/ continuit\u00e9"},"content":{"rendered":"<div id=\"mtq_quiz_area-1\" class=\"mtq_quiz_area mtq_color_blue\"> \r\n  <!--Quiz generated using mTouch Quiz Version 3.1.3 by G. Michael Guy (http:\/\/gmichaelguy.com\/quizplugin\/)-->\r\n        \r\n      \r\n  <!-- Shortcode entered mtouchquiz id=3 --> \r\n  <!-- Shortcode interpreted mtouchquiz id=3 alerts=on singlepage=on hints=off startscreen=on finalscreen=on multiplechances=off showanswers=now show_stamps=on randomq=on randoma=on status=on labels=on title=on proofread=off list=off time=off scoring=off formid= vform=on autoadvance=off autosubmit=off inform=off forcecf=off forcegf=off offset=1 questions=11 firstid=19 lastid=29 color=blue --> \r\n  <!--form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-3\"-->\r\n    <div id=\"mtq_quiztitle-1\" class=\"mtq_quiztitle\" >\r\n  <h2>Convexit\u00e9 \/ Continuit\u00e9<\/h2>\r\n  <\/div>\r\n      <noscript>\r\n  <div id=\"mtq_javawarning-1\" class=\"mtq_javawarning\">\r\n  Veuillez attendre la fin du chargement de l'activit\u00e9. <\/br>Si l'activit\u00e9 se ne charge pas, essayez de rafra\u00eechir votre navigateur. Cette page n\u00e9cessite aussi Javascript. Veuillez la visiter avec Javascript activ\u00e9.  <div class=\"mtq_failed_button\" onclick=\"mtq_start_one(1)\">\r\n  Si le chargement \u00e9choue, cliquez ici pour r\u00e9-essayer  <\/div><\/div>\r\n  <\/noscript>\r\n    <div id=\"mtq_instructions-1\" class=\"mtq_instructions\"><\/div> <div id=\"mtq_start_button-1\" class='mtq_action_button mtq_css_button mtq_start_button' onclick='mtq_start_quiz(1)'> <div class=\"mtq_start_text\">\r\n  D\u00e9part  <\/div> <\/div>\r\n  <div id=\"mtq_quiz_results_bubble-1\" class=\"mtq_quiz_results_bubble\"> <div id=\"mtq_quiz_results-1\" class=\"mtq_quiz_results\"><p>F\u00e9licitation - vous avez compl\u00e9t\u00e9 <em>Convexit\u00e9 \/ Continuit\u00e9<\/em>.<\/p><p>Vous avez obtenu  %%SCORE%% sur %%TOTAL%%.<\/p><p>Votre performance a \u00e9t\u00e9 \u00e9valu\u00e9e \u00e0 %%RATING%%<\/p> <br>    \r\n  <\/div> <div id=\"mtq_quiz_results_highlight-1\" class=\"mtq_quiz_results_highlight\">\r\n  Vos r\u00e9ponses sont surlign\u00e9es ci-dessous.  <\/div> <\/div>\r\n    \r\n  <!-- root element for mtqscrollable -->\r\n\r\n  <div id=\"mtq_question_container-1\" style='display:none'>\r\n  <div >\r\n          <div class='mtq_question mtq_scroll_item-1' id='mtq_question-1-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 1<\/div><div id='mtq_stamp-1-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-1-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep5.png\" alt=\"\" width=\"512\" height=\"255\" class=\"alignnone size-full wp-image-115\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nLa courbe ci-dessus repr\u00e9sente la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span>. Parmis ces affirmations une seule est vraie.<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-1-1-1' onclick='mtq_button_click(1,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 1, Choice 1'>A<\/div><div id='mtq_marker-1-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime(x)=0<\/span> admet 1 solution.<\/div><\/td><\/tr><tr id='mtq_row-1-2-1' onclick='mtq_button_click(1,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 1, Choice 2'>B<\/div><div id='mtq_marker-1-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime(x)=0<\/span> admet 3 solutions.<\/div><\/td><\/tr><tr id='mtq_row-1-3-1' onclick='mtq_button_click(1,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 1, Choice 3'>C<\/div><div id='mtq_marker-1-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime(x)=0<\/span> admet 2 solutions.<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-1-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 1:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> admet deux tangentes horizontales donc <span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=0<\/span> admet 2 solutions.<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-2-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 2<\/div><div id='mtq_stamp-2-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-2-1' class='mtq_question_text'>On consid\u00e8re <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> une fonction d\u00e9finie sur <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span> telle que <span class=\"wp-katex-eq\" data-display=\"false\">f(x)=x^2-5x+6<\/span>. Alors l'\u00e9quation de sa tangente au point abscisse <span class=\"wp-katex-eq\" data-display=\"false\">-1<\/span> est \u00e9gale \u00e0 :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-2-1-1' onclick='mtq_button_click(2,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 2, Choice 1'>A<\/div><div id='mtq_marker-2-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">y=-7x+19<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-2-1' onclick='mtq_button_click(2,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 2, Choice 2'>B<\/div><div id='mtq_marker-2-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">y=19x+12<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-3-1' onclick='mtq_button_click(2,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 2, Choice 3'>C<\/div><div id='mtq_marker-2-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">y=-7x+5<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-4-1' onclick='mtq_button_click(2,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 2, Choice 4'>D<\/div><div id='mtq_marker-2-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">y=12x+12<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-2-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 2:&nbsp;<\/div><div class='mtq_explanation-text'> (cf propri\u00e9t\u00e9 2)  <span class=\"wp-katex-eq\" data-display=\"false\">f'(a)(x-a)+f(a)<\/span>, ici <span class=\"wp-katex-eq\" data-display=\"false\">a=-1<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">f'(x)=2x-5<\/span>. Donc <span class=\"wp-katex-eq\" data-display=\"false\">f'(-1)(x-(-1))+f(-1)=(2\\times(-1)-5)(x+1)+12=-7x+5<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-3-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 3<\/div><div id='mtq_stamp-3-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-3-1' class='mtq_question_text'>On consid\u00e8re le tableau de signes suivant \r\n<ol>\r\n<\/ol>\r\n\r\n\r\n<img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep4.png\" alt=\"\" width=\"356\" height=\"88\" class=\"alignnone size-full wp-image-114\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nOn en d\u00e9duit que :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-3-1-1' onclick='mtq_button_click(3,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 3, Choice 1'>A<\/div><div id='mtq_marker-3-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span>  et admet un point d'inflexion au point <span class=\"wp-katex-eq\" data-display=\"false\">(5,f^\\prime(5))<\/span>.<\/div><\/td><\/tr><tr id='mtq_row-3-2-1' onclick='mtq_button_click(3,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 3, Choice 2'>B<\/div><div id='mtq_marker-3-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span> et admet un point d'inflexion au point <span class=\"wp-katex-eq\" data-display=\"false\">(5,f^\\prime(5))<\/span>.<\/div><\/td><\/tr><tr id='mtq_row-3-3-1' onclick='mtq_button_click(3,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 3, Choice 3'>C<\/div><div id='mtq_marker-3-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span> , convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span>  et admet un point d'inflexion au point <span class=\"wp-katex-eq\" data-display=\"false\">(5,f(5))<\/span>.<\/div><\/td><\/tr><tr id='mtq_row-3-4-1' onclick='mtq_button_click(3,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 3, Choice 4'>D<\/div><div id='mtq_marker-3-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span> et admet un point d'inflexion au point <span class=\"wp-katex-eq\" data-display=\"false\">(5,f(5))<\/span>.<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-3-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 3:&nbsp;<\/div><div class='mtq_explanation-text'> cf propri\u00e9t\u00e9 4 et 5<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-4-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 4<\/div><div id='mtq_stamp-4-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-4-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep5.png\" alt=\"\" width=\"512\" height=\"255\" class=\"alignnone size-full wp-image-115\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nLa courbe ci-dessus repr\u00e9sente la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f^{\\prime\\prime}<\/span> d\u00e9finie sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;10]<\/span>. Parmis ces affirmations une seule est vraie.<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-4-1-1' onclick='mtq_button_click(4,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 4, Choice 1'>A<\/div><div id='mtq_marker-4-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;0,5]\\cup[5,3;10]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;5,3]<\/span><\/div><\/td><\/tr><tr id='mtq_row-4-2-1' onclick='mtq_button_click(4,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 4, Choice 2'>B<\/div><div id='mtq_marker-4-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;0,5]\\cup[5,3;10]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;5,3]<\/span><\/div><\/td><\/tr><tr id='mtq_row-4-3-1' onclick='mtq_button_click(4,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 4, Choice 3'>C<\/div><div id='mtq_marker-4-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;1,5]\\cup[8,6;10]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[1,5;8,6]<\/span><\/div><\/td><\/tr><tr id='mtq_row-4-4-1' onclick='mtq_button_click(4,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 4, Choice 4'>D<\/div><div id='mtq_marker-4-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;1,5]\\cup[8,6;10]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[1,5;8,6]<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-4-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 4:&nbsp;<\/div><div class='mtq_explanation-text'> car <span class=\"wp-katex-eq\" data-display=\"false\">f^{\\prime\\prime} (x)\\leqslant 0<\/span> sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;1,5]\\cup[8,6;10]<\/span> et  <span class=\"wp-katex-eq\" data-display=\"false\">f^{\\prime\\prime}(x)\\geqslant 0<\/span> su<span class=\"wp-katex-eq\" data-display=\"false\">[1,5;8,6]<\/span> (cf prorpi\u00e9t\u00e9 5)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-5-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 5<\/div><div id='mtq_stamp-5-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-5-1' class='mtq_question_text'>On consid\u00e8re le tableau de signes suivant \r\n<ol>\r\n<\/ol>\r\n\r\n\r\n<img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep3.png\" alt=\"\" width=\"351\" height=\"93\" class=\"alignnone size-full wp-image-113\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nOn en d\u00e9duit que :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-5-1-1' onclick='mtq_button_click(5,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 5, Choice 1'>A<\/div><div id='mtq_marker-5-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span> et croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span> <\/div><\/td><\/tr><tr id='mtq_row-5-2-1' onclick='mtq_button_click(5,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 5, Choice 2'>B<\/div><div id='mtq_marker-5-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span> et d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span> <\/div><\/td><\/tr><tr id='mtq_row-5-3-1' onclick='mtq_button_click(5,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 5, Choice 3'>C<\/div><div id='mtq_marker-5-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime<\/span> est croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span> et d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span> <\/div><\/td><\/tr><tr id='mtq_row-5-4-1' onclick='mtq_button_click(5,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 5, Choice 4'>D<\/div><div id='mtq_marker-5-4-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime<\/span> est d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;5]<\/span> et croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[5;+\\infty[<\/span> <\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-5-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 5:&nbsp;<\/div><div class='mtq_explanation-text'> Du signe de la d\u00e9riv\u00e9e on peut en d\u00e9duire les variations de la fonction. <span class=\"wp-katex-eq\" data-display=\"false\">f''<\/span> est la fonction d\u00e9riv\u00e9e de <span class=\"wp-katex-eq\" data-display=\"false\">f'<\/span>. (cf Th\u00e9or\u00e8me 2)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-6-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 6<\/div><div id='mtq_stamp-6-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-6-1' class='mtq_question_text'>D\u00e9terminer le tableau de signe la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> d\u00e9finie sur <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span> par <span class=\"wp-katex-eq\" data-display=\"false\">f(x)=2x^2-10x+12<\/span>.\r\n\r\n<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-6-1-1' onclick='mtq_button_click(6,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 6, Choice 1'>A<\/div><div id='mtq_marker-6-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-1-1' class='mtq_answer_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep1-d.png\" alt=\"\" width=\"476\" height=\"99\" class=\"alignnone size-full wp-image-107\" \/><\/div><\/td><\/tr><tr id='mtq_row-6-2-1' onclick='mtq_button_click(6,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 6, Choice 2'>B<\/div><div id='mtq_marker-6-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-2-1' class='mtq_answer_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep1-a.png\" alt=\"\" width=\"476\" height=\"99\" class=\"alignnone size-full wp-image-107\" \/><\/div><\/td><\/tr><tr id='mtq_row-6-3-1' onclick='mtq_button_click(6,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 6, Choice 3'>C<\/div><div id='mtq_marker-6-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-3-1' class='mtq_answer_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep1-c.png\" alt=\"\" width=\"476\" height=\"99\" class=\"alignnone size-full wp-image-107\" \/><\/div><\/td><\/tr><tr id='mtq_row-6-4-1' onclick='mtq_button_click(6,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 6, Choice 4'>D<\/div><div id='mtq_marker-6-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-4-1' class='mtq_answer_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep1-b.png\" alt=\"\" width=\"476\" height=\"99\" class=\"alignnone size-full wp-image-107\" \/><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-6-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 6:&nbsp;<\/div><div class='mtq_explanation-text'> On utilise le discriminant pour trouver les racines et on applique la r\u00e8gle des signes pour une fonction polynomiale du second degr\u00e9.<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-7-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 7<\/div><div id='mtq_stamp-7-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-7-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep6.png\" alt=\"\" width=\"1044\" height=\"674\" class=\"alignnone size-full wp-image-116\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nCi contre la courbe <span class=\"wp-katex-eq\" data-display=\"false\">\\mathscr{C}_f<\/span> repr\u00e9sentation graphique de la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> d\u00e9finie sur <span class=\"wp-katex-eq\" data-display=\"false\">]1,8;18,2[<\/span>, ainsi que ses deux tangentes aux points F et G (points d'abscisses respectives 7,09 et 13,25).\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nParmi ces affirmations une seule est vraie<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-7-1-1' onclick='mtq_button_click(7,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 7, Choice 1'>A<\/div><div id='mtq_marker-7-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]1,8;7,09]\\cup[13,25;18,2[<\/span> et convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[7,09;18,2]<\/span><\/div><\/td><\/tr><tr id='mtq_row-7-2-1' onclick='mtq_button_click(7,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 7, Choice 2'>B<\/div><div id='mtq_marker-7-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]1,8;7,09]\\cup[13,25;18,2[<\/span> et convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[7,09;18,2]<\/span><\/div><\/td><\/tr><tr id='mtq_row-7-3-1' onclick='mtq_button_click(7,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 7, Choice 3'>C<\/div><div id='mtq_marker-7-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]1,8;4,9]\\cup[10;15,5[<\/span> et convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[4,9;10]\\cup[15,5;18,2[<\/span><\/div><\/td><\/tr><tr id='mtq_row-7-4-1' onclick='mtq_button_click(7,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 7, Choice 4'>D<\/div><div id='mtq_marker-7-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]1,8;4,9]\\cup[10;15,5[<\/span> et concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[4,9;10]\\cup[15,5;18,2[<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-7-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 7:&nbsp;<\/div><div class='mtq_explanation-text'> Il faut regarder la position des tangentes par rapport \u00e0 la courbe. (cf d\u00e9finition 2)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-8-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 8<\/div><div id='mtq_stamp-8-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-8-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/ch2-a.png\" alt=\"\" width=\"690\" height=\"606\" class=\"alignnone size-full wp-image-106\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\n\r\nCi dessus <span class=\"wp-katex-eq\" data-display=\"false\">\\mathscr{C}_f<\/span> (la courbe repr\u00e9sent\u00e9e en rouge ) et sa tangente <span class=\"wp-katex-eq\" data-display=\"false\">\\Delta<\/span> passant par le point <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> (repr\u00e9sent\u00e9e en noir). L'\u00e9quation de cette tangente est \u00e9gale \u00e0 :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-8-1-1' onclick='mtq_button_click(8,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 8, Choice 1'>A<\/div><div id='mtq_marker-8-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\Delta : y= \\dfrac{1}{2}x+1<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-2-1' onclick='mtq_button_click(8,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 8, Choice 2'>B<\/div><div id='mtq_marker-8-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\Delta : y= 2x+1<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-3-1' onclick='mtq_button_click(8,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 8, Choice 3'>C<\/div><div id='mtq_marker-8-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\Delta : y= -2x+1<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-4-1' onclick='mtq_button_click(8,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 8, Choice 4'>D<\/div><div id='mtq_marker-8-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\Delta : y=  -\\dfrac{1}{2}x+1<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-8-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 8:&nbsp;<\/div><div class='mtq_explanation-text'> Une droite a une \u00e9quation de la forme <span class=\"wp-katex-eq\" data-display=\"false\">y=mx+p<\/span>.\r\nL'ordonn\u00e9e \u00e0 l'origine de la droite vaut <span class=\"wp-katex-eq\" data-display=\"false\">p=1<\/span>.\r\nOn consid\u00e8re le point <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> et le point <span class=\"wp-katex-eq\" data-display=\"false\">B(-0,5;0)<\/span> appartenant \u00e0 la droite.\r\n<span class=\"wp-katex-eq\" data-display=\"false\">m=\\dfrac{y_A-y_B}{x_A-x_B}=\\dfrac{1-0}{0-(-0,5)}=2<\/span>\r\nDonc <span class=\"wp-katex-eq\" data-display=\"false\">\\Delta : y= 2x+1<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-9-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 9<\/div><div id='mtq_stamp-9-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-9-1' class='mtq_question_text'>On consid\u00e8re le tableau de variation suivant :\r\n<ol>\r\n<\/ol>\r\n\r\n\r\n<img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep2.png\" alt=\"\" width=\"366\" height=\"129\" class=\"alignnone size-full wp-image-111\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nOn en d\u00e9duit que :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-9-1-1' onclick='mtq_button_click(9,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 9, Choice 1'>A<\/div><div id='mtq_marker-9-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-1-1' class='mtq_answer_text'>On ne peut rien en d\u00e9duire<\/div><\/td><\/tr><tr id='mtq_row-9-2-1' onclick='mtq_button_click(9,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 9, Choice 2'>B<\/div><div id='mtq_marker-9-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-2-1' class='mtq_answer_text'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[0;\\dfrac{\\pi}{2}]<\/span> et convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[\\dfrac{\\pi}{2};1]<\/span>. Elle admet aussi un point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(\\dfrac{\\pi}{2};f(1))<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-3-1' onclick='mtq_button_click(9,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 9, Choice 3'>C<\/div><div id='mtq_marker-9-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-3-1' class='mtq_answer_text'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur  <span class=\"wp-katex-eq\" data-display=\"false\">[0;1]<\/span> car <span class=\"wp-katex-eq\" data-display=\"false\">f'(x)\\geqslant<\/span> sur <span class=\"wp-katex-eq\" data-display=\"false\">[0;1]<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-4-1' onclick='mtq_button_click(9,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 9, Choice 4'>D<\/div><div id='mtq_marker-9-4-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-4-1' class='mtq_answer_text'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[0;\\dfrac{\\pi}{2}]<\/span> et concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[\\dfrac{\\pi}{2};1]<\/span>.  Elle admet aussi un point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(\\dfrac{\\pi}{2};f(1))<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-9-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 9:&nbsp;<\/div><div class='mtq_explanation-text'> (cf propri\u00e9t\u00e9 3)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-10-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 10<\/div><div id='mtq_stamp-10-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-10-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep5.png\" alt=\"\" width=\"512\" height=\"255\" class=\"alignnone size-full wp-image-115\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nLa courbe ci-dessus repr\u00e9sente la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime<\/span> d\u00e9finie sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;10]<\/span>. Parmis ces affirmations une seule est vraie.<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-10-1-1' onclick='mtq_button_click(10,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-10-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 10, Choice 1'>A<\/div><div id='mtq_marker-10-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-10-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;0,5]\\cup[5,3;10]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;5,3]<\/span><\/div><\/td><\/tr><tr id='mtq_row-10-2-1' onclick='mtq_button_click(10,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-10-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 10, Choice 2'>B<\/div><div id='mtq_marker-10-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-10-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;1,5]\\cup[8,6;10]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[1,5;8,6]<\/span><\/div><\/td><\/tr><tr id='mtq_row-10-3-1' onclick='mtq_button_click(10,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-10-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 10, Choice 3'>C<\/div><div id='mtq_marker-10-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-10-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;1,5]\\cup[8,6;10]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[1,5;8,6]<\/span><\/div><\/td><\/tr><tr id='mtq_row-10-4-1' onclick='mtq_button_click(10,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-10-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 10, Choice 4'>D<\/div><div id='mtq_marker-10-4-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-10-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;0,5]\\cup[5,3;10]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;5,3]<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-10-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 10:&nbsp;<\/div><div class='mtq_explanation-text'> car <span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)<\/span> est d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]0;0,5]\\cup[5,3;10]<\/span>, et <span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)<\/span> est croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;5,3]<\/span> (cf propri\u00e9t\u00e9 3)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-11-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 11<\/div><div id='mtq_stamp-11-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-11-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep6.png\" alt=\"\" width=\"1044\" height=\"674\" class=\"alignnone size-full wp-image-116\" \/>\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nCi contre la courbe <span class=\"wp-katex-eq\" data-display=\"false\">\\mathscr{C}_f<\/span> repr\u00e9sentation graphique de la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> d\u00e9finie sur <span class=\"wp-katex-eq\" data-display=\"false\">]1,8;18,2[<\/span>, ainsi que ses deux tangentes aux points F et G (points d'abscisses respectives 7,09 et 13,25).\r\n<ol>\r\n<\/ol>\r\n\r\n\r\nParmi ces affirmations une seule est vraie<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-11-1-1' onclick='mtq_button_click(11,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-11-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 11, Choice 1'>A<\/div><div id='mtq_marker-11-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-11-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> admet 2 points d'inflexions.<\/div><\/td><\/tr><tr id='mtq_row-11-2-1' onclick='mtq_button_click(11,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-11-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 11, Choice 2'>B<\/div><div id='mtq_marker-11-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-11-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> admet 3 points d'inflexions.<\/div><\/td><\/tr><tr id='mtq_row-11-3-1' onclick='mtq_button_click(11,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-11-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 11, Choice 3'>C<\/div><div id='mtq_marker-11-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-11-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> n'admet pas de point d'inflexion.<\/div><\/td><\/tr><tr id='mtq_row-11-4-1' onclick='mtq_button_click(11,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-11-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 11, Choice 4'>D<\/div><div id='mtq_marker-11-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-11-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> admet 1 point d'inflexion.<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-11-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 11:&nbsp;<\/div><div class='mtq_explanation-text'> Il n'y a que deux tangentes qui traversent la courbe. Donc <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> admet 2 points d'inflexions. (cf d\u00e9finition 3)<\/div><\/div><\/div>            <div id=\"mtq_results_request-1\" class=\"mtq_results_request mtq_scroll_item-1\">\r\n        Une fois termin\u00e9, cliquez sur le bouton ci-dessous. Toutes les questions que vous n'avez pas compl\u00e9t\u00e9es sont marqu\u00e9es comme incorrectes.        <span id=\"mtq_results_button-1\" class='mtq_action_button mtq_css_button mtq_results_button'  onclick='mtq_get_results(1)'> <span class=\"mtq_results_text\">\r\n        Obtenir les r\u00e9sultats        <\/span> <\/span> <\/div>\r\n                <!--End of mtqscrollable items--> \r\n    \r\n  <\/div>\r\n  <!--End of mtqscrollable--> \r\n  <!--mtq_status-->\r\n    <div id=\"mtq_quiz_status-1\" class=\"mtq_quiz_status\">\r\n  Il y a 11 questions \u00e0 compl\u00e9ter.  <\/div>\r\n      <\/div> \r\n  <!--Holds all questions-->\r\n    <div id=\"mtq_variables\" class=\"mtq_preload\" style=\"display:none\"> <input type='hidden' id='mtq_id-1' name='mtq_id_value' value='1' \/><input type='hidden' name='question_id[]' value='25'\/><input type='hidden' id='mtq_is_answered-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-1' value='0'\/><input type='hidden' id='mtq_is_worth-1-1' 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value='0'\/><input type='hidden' id='mtq_was_ever_selected-11-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-11-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-11-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-11-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-11-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-11-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-11-1' value='4' \/><input type='hidden' id='mtq_num_correct-11-1' value='1' \/> <div id=\"mtq_have_completed_string\" class=\"mtq_preload\">\r\n    Vous avez compl\u00e9t\u00e9    <\/div> <div id=\"mtq_questions_string\" class=\"mtq_preload\">\r\n    questions    <\/div> <div id=\"mtq_question_string\" class=\"mtq_preload\">\r\n    question    <\/div> <div id=\"mtq_your_score_is_string\"  class=\"mtq_preload\">\r\n    Votre score est de    <\/div> <div id=\"mtq_correct_string\"  class=\"mtq_preload\">\r\n    Correct    <\/div> <div id=\"mtq_wrong_string\"  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Si vous quittez cette page, votre progression sera perdue.    <\/div> <div id='mtq_correct_answer_string' class='mtq_preload'>\r\n    R\u00e9ponses correctes    <\/div> <div id='mtq_you_selected_string' class='mtq_preload'>\r\n    Vous avez s\u00e9lectionn\u00e9    <\/div> <div id='mtq_not_attempted_string' class='mtq_preload'>\r\n    Pas essayer    <\/div> <div id='mtq_final_score_on_quiz_string' class='mtq_preload'>\r\n    Score final du quiz    <\/div> <div id='mtq_attempted_questions_correct_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re correcte    <\/div> <div id='mtq_attempted_questions_wrong_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re incorrecte    <\/div> <div id='mtq_questions_not_attempted_string' class='mtq_preload'>\r\n    Question non r\u00e9pondues    <\/div> <div id='mtq_total_questions_on_quiz_string' class='mtq_preload'>\r\n    Nombre total de questions dans le quiz    <\/div> <div 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