Quiz — DC2.4.14-15-M.pdf

Question 1 sur 10 20:00

[{"id":16609,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 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\": \"A. 6x + 2\", \"b\": \"B. 3x + 2\", \"c\": \"C. 6x² + 2\", \"d\": \"D. 6x - 5","_debug_options_count":4},{"id":16610,"question":"Si une fonction est continue sur un intervalle, elle est nécessairement dérivable sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction continue n'est pas forcément dérivable (exemple : f(x) = |x| en x=0). La dérivabilité implique la continuité, mais l'inverse n'est pas vrai.","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":16611,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"A. 16","option_b":"B. 8","option_c":"C. 32","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 4x³ est x⁴. Entre 0 et 2 : 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 16\", \"b\": \"B. 8\", \"c\": \"C. 32\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":16612,"question":"La limite de f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"Factorisons le numérateur : (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1. Donc la limite est 1+1 = 2. (Réponse C corrigée : la bonne réponse est 2, mais ici l'option C est 2, donc correct=2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. 2\", \"d\": \"D. Indéterminée\"}}","_debug_options_count":4},{"id":16613,"question":"L'intégrale d'une fonction positive entre a et b représente :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une fonction positive entre a et b représente l'aire sous la courbe entre ces deux points.","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":16614,"question":"Quelle est la dérivée de f(x) = ln(x) ?","option_a":"A. 1\/x","option_b":"B. x","option_c":"C. e^x","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, une formule fondamentale à retenir.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 1\/x\", \"b\": \"B. x\", \"c\": \"C. e^x\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":16615,"question":"Si f'(x) = 0 pour tout x dans un intervalle, alors f est constante sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si la dérivée est nulle sur un intervalle, la fonction est constante sur cet intervalle (théorème des accroissements finis).","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":16616,"question":"Quelle est la primitive de f(x) = 5x⁴ ?","option_a":"A. x⁵ + C","option_b":"B. 20x³ + C","option_c":"C. 5x⁵\/5 + C","option_d":"D. x⁴ + C","option_e":"","option_f":"","bonne_reponse":"c","explication":"La primitive de xⁿ est x^(n+1)\/(n+1). Donc 5x⁴ a pour primitive 5*(x⁵\/5) = x⁵ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. x⁵ + C\", \"b\": \"B. 20x³ + C\", \"c\": \"C. 5x⁵\/5 + C\", \"d\": \"D","_debug_options_count":4},{"id":16617,"question":"La fonction f(x) = 1\/x est continue sur ℝ* mais pas dérivable en x=0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 1\/x n'est pas définie en x=0, donc elle n'est ni continue ni dérivable en ce point.","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":16618,"question":"Quelle est l'aire sous la courbe de f(x) = 2x entre 0 et 3 ?","option_a":"A. 6","option_b":"B. 9","option_c":"C. 3","option_d":"D. 18","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x entre 0 et 3 est [x²] de 0 à 3 = 9 - 0 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 6\", \"b\": \"B. 9\", \"c\": \"C. 3\", \"d\": \"D. 18\"}}","_debug_options_count":4}]