Quiz — Lycée Pilote Ariana - Dérivabilité.pdf

Question 1 sur 5 10:00

[{"id":178,"question":"Soit la fonction f(x) = x². Quel est le nombre dérivé de f en x = 3 ?","option_a":"3","option_b":"6","option_c":"9","option_d":"12","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le nombre dérivé f'(a) est la limite du taux d'accroissement [f(a+h)-f(a)]\/h quand h tend vers 0. Pour f(x)=x², f'(x)=2x, donc f'(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":179,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"e^(2x)","option_b":"2e^(2x)","option_c":"2x e^(2x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^u est u'e^u. Ici u=2x, donc u'=2, d'où f'(x)=2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"e^(2x)\", \"b\": \"2e^(2x)\", \"c\": \"2x e^(2x)\", \"d\": \"e^(x)\"}}","_debug_options_count":4},{"id":180,"question":"Si f'(x) = 3x² - 4x + 1, quelle est la fonction f(x) ?","option_a":"x³ - 2x² + x + C","option_b":"x³ - 2x² + x","option_c":"3x³ - 4x² + x + C","option_d":"x³ - 4x² + x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de f'(x) s'obtient par intégration terme à terme. ∫3x² dx = x³, ∫-4x dx = -2x², ∫1 dx = x. La constante C est indéterminée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x³ - 2x² + x + C\", \"b\": \"x³ - 2x² + x\", \"c\": \"3x³ - 4x² + x","_debug_options_count":4},{"id":181,"question":"Soit f(x) = (2x+1)\/(x-3). Quel est le domaine de dérivabilité de f ?","option_a":"R","option_b":"R \\ {3}","option_c":"R \\ {-1\/2}","option_d":"R \\ {3, -1\/2}","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction est dérivable sur son domaine de définition, soit R privé du point où le dénominateur s'annule : x-3=0 ⇒ x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"R\", \"b\": \"R \\\\ {3}\", \"c\": \"R \\\\ {-1\/2}\", \"d\": \"R \\\\ {3, -1\/2}\"}}","_debug_options_count":4},{"id":182,"question":"Quelle est la dérivée de f(x) = ln(5x² + 1) ?","option_a":"10x\/(5x²+1)","option_b":"5x\/(5x²+1)","option_c":"(5x²+1)\/10x","option_d":"10x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici u=5x²+1, donc u'=10x. D'où f'(x)=10x\/(5x²+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\": \"10x\/(5x²+1)\", \"b\": \"5x\/(5x²+1)\", \"c\": \"(5x²+1)\/10x\", \"d\": \"10x","_debug_options_count":4}]