Quiz : Maîtrisez les fonctions numériques en Terminale Maths

Question 1 sur 10 10:00

[{"id":68752,"question":"Soit f(x) = x³ - 3x² + 2. Que vaut f'(x) ?","option_a":"3x² - 6x","option_b":"3x² - 3x + 2","option_c":"x² - 3x","option_d":"3x² - 6x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -3x² est -6x, et celle de 2 est 0. Donc f'(x) = 3x² - 6x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68753,"question":"La fonction f(x) = 1\/x admet une asymptote verticale en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction 1\/x tend vers ±∞ quand x tend vers 0, donc elle admet bien une asymptote verticale en x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68754,"question":"Soit f(x) = e^x. Que vaut f'(x) ?","option_a":"e^x","option_b":"x·e^x","option_c":"e^x + 1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction exponentielle e^x est elle-même : f'(x) = e^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68755,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction logarithme ln(x) n'est définie que pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68756,"question":"Soit f(x) = x² - 4x + 3. Quel est le minimum de cette fonction ?","option_a":"-1","option_b":"0","option_c":"1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2. En étudiant le signe de f'(x), on voit que f admet un minimum en x = 2. f(2) = 4 - 8 + 3 = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68757,"question":"La fonction f(x) = sin(x) est périodique de période 2π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction sinus est bien périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68758,"question":"Soit f(x) = (2x + 1)\/(x - 3). Quelle est l'asymptote horizontale de cette fonction ?","option_a":"y = 2","option_b":"y = 0","option_c":"y = x - 3","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant le numérateur et le dénominateur par x, on obtient f(x) = (2 + 1\/x)\/(1 - 3\/x). Quand x tend vers ±∞, 1\/x tend vers 0, donc f(x) tend vers 2\/1 = 2. L'asymptote horizontale est donc y = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68760,"question":"La fonction f(x) = x^4 admet un point d'inflexion en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée seconde f''(x) = 12x² est toujours positive ou nulle, donc la fonction est toujours convexe. Il n'y a pas de point d'inflexion.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68762,"question":"Soit f(x) = x·ln(x). Que vaut f'(x) ?","option_a":"ln(x) + 1","option_b":"x + ln(x)","option_c":"1\/ln(x)","option_d":"x·ln(x) + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de dérivation d'un produit (uv)' = u'v + uv', on obtient f'(x) = 1·ln(x) + x·(1\/x) = ln(x) + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68764,"question":"La fonction f(x) = √x est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de √x est 1\/(2√x). En x = 0, cette dérivée tend vers +∞, donc la fonction n'est pas dérivable en 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]