Quiz : Maîtrisez les fonctions dérivées et les suites en Terminale Math

Question 1 sur 10 10:00

[{"id":43776,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule en appliquant la règle de dérivation terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43777,"question":"Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite croissante n'est pas nécessairement convergente. Par exemple, la suite uₙ = n est croissante mais diverge vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43778,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) lorsque x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour trouver la limite à l'infini, on compare les termes de plus haut degré : lim (2x\/x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43779,"question":"La fonction f(x) = x³ - 3x² + 2 est convexe sur l'intervalle [-1, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La convexité se détermine avec la dérivée seconde : f''(x) = 6x - 6. f''(x) \u003C 0 sur [-1, 2], donc la fonction est concave sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43780,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 2 ou x = 1\/2","option_b":"x = -2 ou x = 1\/2","option_c":"x = 2 ou x = -1\/2","option_d":"x = -2 ou x = -1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant le discriminant Δ = 25 - 16 = 9, on obtient x = (5 ± 3)\/4, soit x = 2 ou x = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43781,"question":"La suite définie par uₙ = (-1)ⁿ est bornée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite uₙ = (-1)ⁿ prend uniquement les valeurs -1 et 1, donc elle est bornée par -1 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43782,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² au point d'abscisse 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":"L'équation de la tangente est y = f'(a)(x - a) + f(a). Ici, f'(1) = 2 et f(1) = 1, donc y = 2(x - 1) + 1 = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43783,"question":"Toute fonction continue sur un intervalle fermé est 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 nécessairement dérivable. Par exemple, f(x) = |x| est continue mais non dérivable en x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43784,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"3e^(3x)","option_b":"e^(3x)","option_c":"3x e^(3x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la règle de dérivation des fonctions exponentielles, f'(x) = 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43785,"question":"La suite uₙ = 1\/n converge vers 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout ε \u003E 0, il existe N tel que pour n ≥ N, |1\/n - 0| \u003C ε. Donc la suite converge vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]