Bonjour,
1)
f(x) = 3x + 5
f'(x) = 3
f'(0) = 3
f(x) = 5x³ - 0,3x + 2
f'(x) = 15x² - 0,3
f'(0) = 0
f(x) = x/(x+2)
f'(x) = [(x+2) - x]/(x+2)² = 2/(x+2)²
f'(0) = 1/2
f(x) = 3x + 5/x
f'(x) = 3 - 5/x²
f'(0) n'existe pas, tend vers ∞
f(x) = 2 + (x+1)/(x²+3)
f'(x) = [(x²+3) - 2x(x+1)]/(x²+3)² = (-x² - 2x + 3)/(x² + 3)
f'(0) = 1
Exercice 2
1)
f(-3) = 5,5
f(0) = 1
f(4) = 3
2)
f'(-3) = 0 tangente horizontale
f'(-1) = -2 pente de la droite tracée
f'(2) = 0 tangente horizontale
3)
x -6 -3 2 4
f(x) -5 crois. 5,5 décrois. -1,3 crois. 3
4) Maximum = f(-3) = 5,5 (environ)
