extreme f(x)=2x^2(x^2-2)

Lösung

extrempunkte

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

Minimum (- 1, - 2), Maximum (0, 0), Minimum (1, - 2)

Schritte zur Lösung

f^{'} (x) = 2 (4 x^{3} - 4 x)

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

2 x^{2} (x^{2} - 2) : - 2

Minimum (- 1, - 2)

Stecke

x = 0

2 x^{2} (x^{2} - 2) : 0

Maximum (0, 0)

Stecke

x = 1

2 x^{2} (x^{2} - 2) : - 2

Minimum (1, - 2)

Minimum (- 1, - 2), Maximum (0, 0), Minimum (1, - 2)

e x t re m e - 3 x + ln (x)

e x t re m e f (x) = 52 (70 - x)

e x t re m e f (x) = x^{11} - 9 x^{7} + 5 x - 3

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

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