extreme f(x)=-3+8x-x^3

Lösung

extrempunkte

f (x) = - 3 + 8 x - x^{3}

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 3), Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 3)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 8

Intervalle finden:

Absteigend

: - \infty < x < - \frac{2 2}{3},

Ansteigend

: - \frac{2 2}{3} < x < \frac{2 2}{3},

Absteigend

: \frac{2 2}{3} < x < \infty

Stecke

x = - \frac{2 2}{3}

- 3 + 8 x - x^{3} : - \frac{32 2}{3 3} - 3

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 3)

Stecke

x = \frac{2 2}{3}

- 3 + 8 x - x^{3} : \frac{32 2}{3 3} - 3

Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 3)

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 3), Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 3)

e x t re m e f (x) = \frac{x + 1}{x ^{2} - 2 x - 3}

e x t re m e f (x, y) = 7 x^{2} - 10 y^{2}

e x t re m e y = \frac{3 x}{x ^{2} - 1}

e x t re m e x^{3} + 6 x^{2} + 12 x + 7

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