Quiz — CORDS1-4S-20-21-final.docx

Question 1 sur 10 20:00

[{"id":39880,"question":"Quelle est la dérivée de la fonction f(x) = 3x⁴ - 2x² + 5 ?","option_a":"A. 12x³ - 4x","option_b":"B. 12x³ - 4x + 5","option_c":"C. 3x³ - 2x + 5","option_d":"D. 12x³ - 4x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de xⁿ est n·xⁿ⁻¹. Ainsi, f'(x) = 3·4x³ - 2·2x = 12x³ - 4x.","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. 12x³ - 4x\", \"b\": \"B. 12x³ - 4x + 5\", \"c\": \"C. 3x³ - 2x + 5\"","_debug_options_count":4},{"id":39881,"question":"Si f'(x) \u003E 0 pour tout x ∈ ℝ, alors la fonction f est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : si la dérivée est positive sur un intervalle, la fonction est strictement croissante 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},{"id":39882,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)(x² - 3) ?","option_a":"A. 4x + 2","option_b":"B. 6x² + 2x - 6","option_c":"C. 2x² - 6x + 2x - 3","option_d":"D. 4x² + 2x - 6","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la règle du produit : f'(x) = 2(x² - 3) + (2x + 1)(2x) = 2x² - 6 + 4x² + 2x = 6x² + 2x - 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\": \"A. 4x + 2\", \"b\": \"B. 6x² + 2x - 6\", \"c\": \"C. 2x² - 6x + 2x - 3\"","_debug_options_count":4},{"id":39883,"question":"La dérivée de la fonction f(x) = 1\/x est toujours négative.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : f'(x) = -1\/x², et x² est toujours positif pour x ≠ 0, donc f'(x) \u003C 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":39884,"question":"Quelle est la dérivée de la fonction f(x) = √(3x + 2) ?","option_a":"A. 3\/(2√(3x + 2))","option_b":"B. 1\/(2√(3x + 2))","option_c":"C. 3\/(√(3x + 2))","option_d":"D. 1\/√(3x + 2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de la dérivée d'une fonction composée : f'(x) = (1\/(2√(3x + 2))) · 3 = 3\/(2√(3x + 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. 3\/(2√(3x + 2))\", \"b\": \"B. 1\/(2√(3x + 2))\", \"c\": \"C. 3\/(√","_debug_options_count":4},{"id":39885,"question":"Si f'(a) = 0 et f''(a) \u003E 0, alors la fonction f admet un minimum local en x = a.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : si la dérivée seconde est positive en un point critique, la fonction admet un minimum local en ce point.","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":39886,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x + 1) ?","option_a":"A. e^(2x + 1)","option_b":"B. 2e^(2x + 1)","option_c":"C. (2x + 1)e^(2x)","option_d":"D. e^(2x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la règle de la dérivée d'une fonction exponentielle composée : f'(x) = 2e^(2x + 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\": \"A. e^(2x + 1)\", \"b\": \"B. 2e^(2x + 1)\", \"c\": \"C. (2x + 1)e^(2x)\", ","_debug_options_count":4},{"id":39887,"question":"La dérivée de la fonction f(x) = sin(2x) est f'(x) = 2cos(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : en utilisant la règle de la dérivée d'une fonction trigonométrique composée, f'(x) = 2cos(2x).","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":39888,"question":"Quelle est la dérivée de la fonction f(x) = ln(5x² + 1) ?","option_a":"A. 10x\/(5x² + 1)","option_b":"B. 1\/(5x² + 1)","option_c":"C. 10x","option_d":"D. 5x\/(5x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de la dérivée d'une fonction logarithme composée : 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\": \"A. 10x\/(5x² + 1)\", \"b\": \"B. 1\/(5x² + 1)\", \"c\": \"C. 10x\", \"d\": \"","_debug_options_count":4},{"id":39889,"question":"Si f'(x) = 0 pour tout x ∈ ℝ, alors la fonction f est constante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : 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}]