Quiz — 636e17d9e12bf_exercice 7 ( lecture graphique - études des fonctions) (2).pdf

Question 1 sur 10 20:00

[{"id":45878,"question":"Quelle est l'image de 2 par la fonction f définie par f(x) = x² - 3x + 2 ?","option_a":"4","option_b":"0","option_c":"2","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculez f(2) = 2² - 3*2 + 2 = 4 - 6 + 2 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"4\", \"b\": \"0\", \"c\": \"2\", \"d\": \"-2\"}}","_debug_options_count":4},{"id":45879,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur [-1, 1] et croissante ailleurs.","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":45880,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² en x = 3 ?","option_a":"3","option_b":"6","option_c":"9","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est égal à f'(3) = 2*3 = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"6\", \"c\": \"9\", \"d\": \"12\"}}","_debug_options_count":4},{"id":45881,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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":45882,"question":"Quelle est la dérivée de la fonction f(x) = 3x⁴ - 2x² + 5 ?","option_a":"12x³ - 4x","option_b":"12x³ - 4x + 5","option_c":"3x³ - 2x","option_d":"12x³ - 4x²","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée est f'(x) = 12x³ - 4x (dérivée terme à terme).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"12x³ - 4x\", \"b\": \"12x³ - 4x + 5\", \"c\": \"3x³ - 2x\", \"d\": \"12x³","_debug_options_count":4},{"id":45883,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2. Comme f''(x) = 2 \u003E 0, il s'agit bien d'un minimum.","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":45884,"question":"Quel est l'antécédent de 5 par la fonction f(x) = 2x - 1 ?","option_a":"3","option_b":"2","option_c":"4","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvez 2x - 1 = 5 ⇒ 2x = 6 ⇒ x = 3.","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\", \"b\": \"2\", \"c\": \"4\", \"d\": \"1\"}}","_debug_options_count":4},{"id":45885,"question":"La fonction f(x) = |x| est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car elle présente un point anguleux.","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":45886,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² en x = 1 ?","option_a":"y = 2x - 1","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1) = 2(x - 1) + 1 = 2x - 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\": \"y = 2x - 1\", \"b\": \"y = x + 1\", \"c\": \"y = 2x + 1\", \"d\": \"y = x - 1","_debug_options_count":4},{"id":45887,"question":"La fonction f(x) = x³ + x est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² + 1 est toujours positive (car 3x² ≥ 0 et 1 \u003E 0), donc la fonction est strictement croissante.","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}]