extreme f(x)=-(x^3)/3-2x^2+5x-2

Lösung

extrempunkte

f (x) = - \frac{x ^{3}}{3} - 2 x^{2} + 5 x - 2

Minimum (- 5, - \frac{106}{3}), Maximum (1, \frac{2}{3})

Schritte zur Lösung

f^{'} (x) = - x^{2} - 4 x + 5

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 1,

Absteigend

: 1 < x < \infty

Stecke

x = - 5

- \frac{x ^{3}}{3} - 2 x^{2} + 5 x - 2 : - \frac{106}{3}

Minimum (- 5, - \frac{106}{3})

Stecke

x = 1

- \frac{x ^{3}}{3} - 2 x^{2} + 5 x - 2 : \frac{2}{3}

Maximum (1, \frac{2}{3})

Minimum (- 5, - \frac{106}{3}), Maximum (1, \frac{2}{3})

e x t re m e f (x) = 2 x^{3} - 4 x^{2} + 2 x + 1

e x t re m e 4 - 3 x - x^{3}

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

e x t re m e - 2 x^{2} + 4 x + 8

e x t re m e f (x y) = x^{2} + 2 y^{2} - x y + 14 y