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[{"id":18408,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"3x² - 4x + 5","option_b":"x² - 2x + 5","option_c":"3x² - 4x + 1","option_d":"2x - 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -2x² est -4x, celle de 5x est 5, et celle de -1 est 0. On additionne les termes pour obtenir 3x² - 4x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18409,"question":"Si f'(x) \u003E 0 sur un intervalle, alors la fonction f est...","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"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},{"id":18410,"question":"Quelle est la limite de f(x) = (2x² + 3x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les limites en ±∞, on compare les termes de plus haut degré : (2x²)\/(x²) = 2. Les autres termes deviennent négligeables.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18411,"question":"La fonction f(x) = ln(x) est définie pour...","option_a":"x \u003E 0","option_b":"x ≥ 0","option_c":"x ∈ ℝ","option_d":"x ≠ 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18412,"question":"Si lim(x→a) f(x) = +∞, alors la droite d'équation x = a est...","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une limite infinie en un point a indique une asymptote verticale d'équation x = a.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18413,"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(x)) est u'(x) * e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2. D'où f'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18414,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x =...","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"C","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2. Comme f''(x) = 2 \u003E 0, c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18415,"question":"Si f est dérivable en a, alors f est continue en a.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction dérivable en un point est nécessairement continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18416,"question":"Quelle est l'équation de l'asymptote oblique de f(x) = (x² + 1)\/x en +∞ ?","option_a":"y = x","option_b":"y = x + 1\/x","option_c":"y = x - 1","option_d":"y = 1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant, f(x) = x + 1\/x. Quand x→+∞, 1\/x→0, donc l'asymptote oblique est y = x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18417,"question":"Le théorème des valeurs intermédiaires s'applique à une fonction...","option_a":"dérivable","option_b":"continue","option_c":"polynomiale","option_d":"strictement monotone","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème des valeurs intermédiaires nécessite que la fonction soit continue sur l'intervalle considéré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]