Quiz — M-CO-VAR-JMF.pdf

Question 1 sur 10 20:00

[{"id":35690,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 6x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction 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\": \"f'(x) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x² + 2x\",","_debug_options_count":4},{"id":35691,"question":"Si f'(x) \u003E 0 sur un intervalle, alors la fonction f est décroissante sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si f'(x) \u003E 0, la fonction f est croissante. Si f'(x) \u003C 0, elle 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":35692,"question":"Quel est le coefficient directeur de la tangente à la courbe de f en x = 1 si f'(1) = 4 ?","option_a":"0","option_b":"1","option_c":"4","option_d":"Indéterminé","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le coefficient directeur de la tangente en un point est égal à la valeur de la dérivée en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"4\", \"d\": \"Indéterminé\"}}","_debug_options_count":4},{"id":35693,"question":"La fonction f(x) = x³ - 3x² admet un extremum local en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"f'(x) = 3x² - 6x. En x = 2, f'(2) = 0 et f''(2) = 6 \u003E 0, donc c'est un minimum local.","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":35694,"question":"Quelle est la dérivée de la fonction g(x) = sin(x) ?","option_a":"g'(x) = cos(x)","option_b":"g'(x) = -cos(x)","option_c":"g'(x) = sin(x)","option_d":"g'(x) = 1\/cos(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est cos(x), une règle fondamentale en analyse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"g'(x) = cos(x)\", \"b\": \"g'(x) = -cos(x)\", \"c\": \"g'(x) = sin(x)\", \"","_debug_options_count":4},{"id":35695,"question":"Si une fonction est dérivable en un point, alors elle est continue en ce point.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivabilité implique la continuité, mais l'inverse n'est pas toujours vrai.","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":35696,"question":"Quelle est la dérivée de la fonction h(x) = e^(2x) ?","option_a":"h'(x) = e^(2x)","option_b":"h'(x) = 2e^(2x)","option_c":"h'(x) = e^x","option_d":"h'(x) = 2x e^(2x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^(u(x)) est 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\": \"b\", \"options\": {\"a\": \"h'(x) = e^(2x)\", \"b\": \"h'(x) = 2e^(2x)\", \"c\": \"h'(x) = e^x\", \"d\":","_debug_options_count":4},{"id":35697,"question":"Une fonction peut avoir un extremum en un point où sa dérivée n'existe pas.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Exemple : f(x) = |x| en x = 0. La dérivée n'existe pas, mais c'est 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":35698,"question":"Quelle est la dérivée de la fonction k(x) = ln(x) ?","option_a":"k'(x) = 1\/x","option_b":"k'(x) = x","option_c":"k'(x) = ln(x)\/x","option_d":"k'(x) = 1\/ln(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, une règle essentielle en analyse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"k'(x) = 1\/x\", \"b\": \"k'(x) = x\", \"c\": \"k'(x) = ln(x)\/x\", \"d\": \"k'(","_debug_options_count":4},{"id":35699,"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.","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}]