extreme f(x)=-1/3 x^3-x^2-12

Lösung

extrempunkte

f (x) = - \frac{1}{3} x^{3} - x^{2} - 12

Minimum (- 2, - \frac{40}{3}), Maximum (0, - 12)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < \infty

Stecke

x = - 2

- \frac{1}{3} x^{3} - x^{2} - 12 : - \frac{40}{3}

Minimum (- 2, - \frac{40}{3})

Stecke

x = 0

- \frac{1}{3} x^{3} - x^{2} - 12 : - 12

Maximum (0, - 12)

Minimum (- 2, - \frac{40}{3}), Maximum (0, - 12)

e x t re m e f (x) = - \frac{24 x}{x ^{2} + 9}

e x t re m e - 2 x^{2} - 12 x - 17

e x t re m e f (x) = 5 x e^{- x}, 0 \leq x \leq 2

e x t re m e f (x) = 2 x^{3} - 9 x^{2} + 60 x + 8

e x t re m e f (x) = 150 x - 2 x^{3}