extreme x^3-12x+16

Lösung

extrempunkte

x^{3} - 12 x + 16

Maximum (- 2, 32), Minimum (2, 0)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 12

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

x^{3} - 12 x + 16 : 32

Maximum (- 2, 32)

Stecke

x = 2

x^{3} - 12 x + 16 : 0

Minimum (2, 0)

Maximum (- 2, 32), Minimum (2, 0)

e x t re m e x^{3} - 12 x + 12

e x t re m e f (x, y) = x^{2} + 5 x y + y^{2} - 2 x + 4 y + 5

e x t re m e f (x, y) = 9 x y + \frac{1000}{y} + \frac{1000}{x}

e x t re m e f (x) = - 2 x + 6 x^{\frac{2}{3}}, - 8 \leq x \leq 4.5

e x t re m e f (x) = 5 (x^{2} + 4)^{2} (x - 4)^{3}