{"id":40,"date":"2018-07-20T11:43:51","date_gmt":"2018-07-20T09:43:51","guid":{"rendered":"http:\/\/mathquiz.fr\/?page_id=40"},"modified":"2018-07-25T13:08:40","modified_gmt":"2018-07-25T11:08:40","slug":"fonctions-exponentielles","status":"publish","type":"page","link":"https:\/\/mathquiz.fr\/?page_id=40","title":{"rendered":"Fonctions exponentielles"},"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=4 --> \r\n  <!-- Shortcode interpreted mtouchquiz id=4 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=7 firstid=30 lastid=36 color=blue --> \r\n  <!--form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-4\"-->\r\n    <div id=\"mtq_quiztitle-1\" class=\"mtq_quiztitle\" >\r\n  <h2>Fonctions exponentielles<\/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>Fonctions exponentielles<\/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'>La solution de l'\u00e9quation <span class=\"wp-katex-eq\" data-display=\"false\">e^{2x+1}=e^{8x-4}<\/span> est \u00e9gale \u00e0 :<\/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'>Pas de 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_correct_marker' alt='Correct'><\/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\">x=\\dfrac{5}{6}<\/span><\/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_wrong_marker' alt='Faux'><\/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\">x=-\\dfrac{6}{5}<\/span><\/div><\/td><\/tr><tr id='mtq_row-1-4-1' onclick='mtq_button_click(1,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 1, Choice 4'>D<\/div><div id='mtq_marker-1-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=-\\dfrac{5}{6}<\/span><\/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'> (cf propri\u00e9t\u00e9 5) <span class=\"wp-katex-eq\" data-display=\"false\">e^{2x+1}=e^{8x-4}<\/span> est \u00e9quivalent \u00e0 r\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">2x+1=8x-4<\/span> ;\r\n\r\n<ul>\r\n<\/ul>\r\n <span class=\"wp-katex-eq\" data-display=\"false\">2x-8x=-4-1<\/span> ;\r\n\r\n<ul>\r\n<\/ul>\r\n <span class=\"wp-katex-eq\" data-display=\"false\">-6x=-5<\/span> ; \r\n\r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{-5}{-6}=\\dfrac{5}{6}<\/span> <\/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 la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> fonction d\u00e9finie et d\u00e9rivable sur <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span> telle que <span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=(2x+5)e^{7x+8}<\/span>, alors :<\/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'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-\\dfrac{5}{2}]<\/span> et d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[-\\dfrac{5}{2};+\\infty[<\/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'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-\\dfrac{7}{8}]<\/span> et d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[-\\dfrac{7}{8};+\\infty[<\/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'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-\\dfrac{5}{2}]<\/span> et croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[-\\dfrac{5}{2};+\\infty[<\/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'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est d\u00e9croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-\\dfrac{7}{8}]<\/span> et croissante sur <span class=\"wp-katex-eq\" data-display=\"false\">[-\\dfrac{7}{8};+\\infty[<\/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'> Pour tout <span class=\"wp-katex-eq\" data-display=\"false\">x\\in\\mathbb{R}<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">e^{7x+8}&gt;0<\/span>. Par cons\u00e9quent le signe de <span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime<\/span> d\u00e9pend de l'expression <span class=\"wp-katex-eq\" data-display=\"false\">2x+5<\/span>. Or <span class=\"wp-katex-eq\" data-display=\"false\">2x+5\\leqslant 0<\/span> sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-\\dfrac{5}{2}]<\/span> et  <span class=\"wp-katex-eq\" data-display=\"false\">2x+5\\geqslant 0<\/span> sur <span class=\"wp-katex-eq\" data-display=\"false\">[-\\dfrac{5}{2};+\\infty[<\/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'>L'in\u00e9quation <span class=\"wp-katex-eq\" data-display=\"false\">e^{5x-1}\\geqslant e^{2x+1}<\/span> a pour solutions les valeurs appartenant \u00e0 l'intervalle<\/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\">]-\\infty;0]<\/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_correct_marker' alt='Correct'><\/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\">[\\dfrac{2}{3};+\\infty[<\/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_wrong_marker' alt='Faux'><\/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\">]-\\infty;\\dfrac{2}{3}]<\/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\">[0;+\\infty[<\/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 5) <span class=\"wp-katex-eq\" data-display=\"false\">e^{5x-1}\\geqslant e^{2x+1}<\/span> est \u00e9quivalent \u00e0 : \r\n\r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">5x-1\\geqslant 2x+1<\/span>; \r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">5x-2x\\geqslant 1+1<\/span>; \r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">3x\\geqslant 2<\/span>; \r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x\\geqslant \\dfrac{2}{3}<\/span><\/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'>On consid\u00e8re <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> une fonction d\u00e9finie et d\u00e9rivable sur <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span> telle que <span class=\"wp-katex-eq\" data-display=\"false\">f(x)=(2x+1)e^{-2x}<\/span>, alors :<\/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_correct_marker' alt='Correct'><\/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^\\prime (x)=-4xe^{-2x}<\/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^\\prime (x)=2e^{-2x}(2x-1)<\/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_wrong_marker' alt='Faux'><\/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^\\prime (x)=2e^{-2x}(2x+1)<\/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^\\prime (x)=2e^{-2x}(4x+2)<\/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'> La fonction est de la forme <span class=\"wp-katex-eq\" data-display=\"false\">(uv)=u'v+uv'<\/span>. Avec <span class=\"wp-katex-eq\" data-display=\"false\">u(x)=2x+1<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">u^\\prime (x)=2<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">v(x)=e^{-2x}<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">v^\\prime (x)=-2e^{-2x}<\/span>. Par cons\u00e9quent :\r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=2e^{-2x}+(2x+1)(-2e^{-2x})<\/span> On a <span class=\"wp-katex-eq\" data-display=\"false\">2e^{-2x}<\/span>  comme facteur commun.\r\n\r\n\r\n<ul>\r\n<\/ul>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=2e^{-2x}(1-(2x+1))<\/span> ;\r\n\r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=2e^{-2x}(1-2x-1)<\/span> ;\r\n\r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=2e^{-2x}(-2x)<\/span> ;\r\n\r\n\r\n<ul>\r\n<\/ul>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">f^\\prime (x)=-4xe^{-2x}<\/span> <\/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 la fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> fonction d\u00e9finie et deux fois d\u00e9rivable sur <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span> telle que <span class=\"wp-katex-eq\" data-display=\"false\">f^{\\prime\\prime}(x)=(-8x+4)e^{x-2}<\/span>, alors :<\/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_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-1-1' 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\">]-\\infty;0,5]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;+\\infty[<\/span> et admet une point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(0,5;f(0,5))<\/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'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-0,5]<\/span>, concave sur <span class=\"wp-katex-eq\" data-display=\"false\">[-0,5;+\\infty[<\/span> et admet une point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(-0,5;f(-0,5))<\/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'>La fonction <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est concave sur <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;-0,5]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[-0,5;+\\infty[<\/span> et admet une point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(-0,5;f(-0,5))<\/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_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-4-1' 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\">]-\\infty;2]<\/span>, convexe sur <span class=\"wp-katex-eq\" data-display=\"false\">[2;+\\infty[<\/span> et admet une point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(0,5;f(0,5))<\/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'> On regarde le signe de <span class=\"wp-katex-eq\" data-display=\"false\">f^{\\prime\\prime}<\/span>. Pour tout <span class=\"wp-katex-eq\" data-display=\"false\">x\\in\\mathbb{R}<\/span>, l'expression <span class=\"wp-katex-eq\" data-display=\"false\">e^{x-2}&gt;0<\/span>. Par cons\u00e9quent le signe  <span class=\"wp-katex-eq\" data-display=\"false\">f^{\\prime\\prime}<\/span> d\u00e9pend du signe de <span class=\"wp-katex-eq\" data-display=\"false\">-8x+4<\/span>.  <span class=\"wp-katex-eq\" data-display=\"false\">-8x+4=0<\/span>; <span class=\"wp-katex-eq\" data-display=\"false\">-8x=-4<\/span>; <span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{-4}{-8}=0,5<\/span>, donc <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> admet un point d'inflexion de coordonn\u00e9es <span class=\"wp-katex-eq\" data-display=\"false\">(0,5;f(0,5))<\/span>. <span class=\"wp-katex-eq\" data-display=\"false\">-8x+4\\geqslant 0<\/span> sur   <span class=\"wp-katex-eq\" data-display=\"false\">]-\\infty;0,5]<\/span>, donc convexe sur cet intervalle et <span class=\"wp-katex-eq\" data-display=\"false\">-8x+4\\leqslant 0<\/span> sur <span class=\"wp-katex-eq\" data-display=\"false\">[0,5;+\\infty[<\/span>, donc concave sur cet intervalle.<\/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'>Simplifier l'expression <span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{(e^{2}\\times e^{-3})^4}{e^7}<\/span><\/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'><span class=\"wp-katex-eq\" data-display=\"false\">e^{28}<\/span><\/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_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">e^{-28}<\/span><\/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_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">e^{-11}<\/span><\/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'><span class=\"wp-katex-eq\" data-display=\"false\">e^{10}<\/span><\/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'> (cf propri\u00e9t\u00e9 4) <span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{(e^{2}\\times e^{-3})^4}{e^7}=\\dfrac{(e^{2-3})^4}{e^7}=\\dfrac{(e^{-1})^4}{e^7}=\\dfrac{e^{-1\\times 4}}{e^7}=\\dfrac{e^{-4}}{e^7}=e^{-4}\\times e^{-7}=e^{-4-7}=e^{-11}<\/span><\/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'>On consid\u00e8re <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> la fonction d\u00e9finie et d\u00e9rivable sur <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{R}<\/span> tel que <span class=\"wp-katex-eq\" data-display=\"false\">f(x)=e^{2x^2+x}<\/span>. Alors :<\/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_correct_marker' alt='Correct'><\/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^\\prime(x)=(4x+1)e^{2x^2+x}<\/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_wrong_marker' alt='Faux'><\/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^\\prime(x)=(2x+1)e^{2x^2+x}<\/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^\\prime(x)=e^{2x+1}<\/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^\\prime(x)=e^{4x+1}<\/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'> Car <span class=\"wp-katex-eq\" data-display=\"false\">f<\/span> est de la forme <span class=\"wp-katex-eq\" data-display=\"false\">e^u<\/span> qui a pour fonction d\u00e9riv\u00e9e  <span class=\"wp-katex-eq\" data-display=\"false\">u'e^u<\/span>, <span class=\"wp-katex-eq\" data-display=\"false\">u(x)=2x^2+x<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">u^\\prime(x)=4x+1<\/span> (cf propri\u00e9t\u00e9 6)<\/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 7 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='33'\/><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_has_hint-7-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-7-2-1' value='0'\/><input type='hidden' id='mtq_was_selected-7-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-7-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-7-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-7-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-7-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-7-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-7-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-7-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-7-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-7-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-7-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-7-1' value='4' \/><input type='hidden' id='mtq_num_correct-7-1' value='1' \/> <div id=\"mtq_have_completed_string\" class=\"mtq_preload\">\r\n    Vous avez 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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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