Quiz — 56.._enon-bob-rl.pdf

Question 1 sur 10 20:00

[{"id":47418,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'un polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x + 2\", \"b\": \"6x² + 2\", \"c\": \"3x + 2\", \"d\": \"6x - 5\"}}","_debug_options_count":4},{"id":47419,"question":"La dérivée de f(x) = e^(2x) est f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : la dérivée d'une fonction exponentielle composée est f'(x) = u'(x) × e^(u(x)), ici u(x) = 2x donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47420,"question":"Quelle est la dérivée de f(x) = ln(3x + 1) ?","option_a":"3\/(3x+1)","option_b":"1\/(3x+1)","option_c":"3x\/(3x+1)","option_d":"1\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici u = 3x + 1, donc u' = 3, d'où f'(x) = 3\/(3x+1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\/(3x+1)\", \"b\": \"1\/(3x+1)\", \"c\": \"3x\/(3x+1)\", \"d\": \"1\/x\"}}","_debug_options_count":4},{"id":47421,"question":"Si f'(x) \u003E 0 sur un intervalle, alors f est décroissante sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux : si f'(x) \u003E 0, alors f est croissante. Si f'(x) \u003C 0, f est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47422,"question":"Quelle est la dérivée de f(x) = sin(5x) ?","option_a":"5cos(5x)","option_b":"cos(5x)","option_c":"sin(5x)","option_d":"5sin(5x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(u) est u'cos(u). Ici u = 5x, donc u' = 5, d'où f'(x) = 5cos(5x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5cos(5x)\", \"b\": \"cos(5x)\", \"c\": \"sin(5x)\", \"d\": \"5sin(5x)\"}}","_debug_options_count":4},{"id":47423,"question":"La dérivée de f(x) = √x est-elle f'(x) = 1\/(2√x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai : la dérivée de √x = x^(1\/2) est (1\/2)x^(-1\/2) = 1\/(2√x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47424,"question":"Quelle est la dérivée de f(x) = (2x + 1)\/(x - 3) ?","option_a":"2\/(x-3)²","option_b":"(x+7)\/(x-3)²","option_c":"2\/(x-3)","option_d":"(2x+1)\/(x-3)","option_e":"","option_f":"","bonne_reponse":"b","explication":"On utilise la formule de dérivation d'un quotient : (u\/v)' = (u'v - uv')\/v². Ici u = 2x+1, v = x-3, donc u' = 2, v' = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\/(x-3)²\", \"b\": \"(x+7)\/(x-3)²\", \"c\": \"2\/(x-3)\", \"d\": \"(2x+1)\/(x","_debug_options_count":4},{"id":47425,"question":"Si f'(a) = 0, alors la tangente à la courbe de f en x = a est parallèle à l'axe des abscisses.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai : une dérivée nulle en un point signifie que la pente de la tangente est nulle, donc elle est horizontale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47426,"question":"Quelle est la dérivée de f(x) = x³ - 4x² + 5x - 2 ?","option_a":"3x² - 8x + 5","option_b":"3x² - 8x - 2","option_c":"x³ - 4x² + 5","option_d":"3x² - 4x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"On dérive terme à terme : (x³)' = 3x², (-4x²)' = -8x, (5x)' = 5, et (-2)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3x² - 8x + 5\", \"b\": \"3x² - 8x - 2\", \"c\": \"x³ - 4x² + 5\", \"d\":","_debug_options_count":4},{"id":47427,"question":"La dérivée d'une fonction constante est toujours nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai : une fonction constante f(x) = k a une dérivée f'(x) = 0 pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]