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Beliebt Funktionen >

extreme f(x)=-x^4+4x^2-2

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

f^{'} (x) = - 4 x^{3} + 8 x

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 2

in

- x^{4} + 4 x^{2} - 2 : 2

Maximum (- 2, 2)

Stecke

x = 0

in

- x^{4} + 4 x^{2} - 2 : - 2

Minimum (0, - 2)

Stecke

x = 2

in

- x^{4} + 4 x^{2} - 2 : 2

Maximum (2, 2)

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

Graph

Beliebte Beispiele

extreme f(x,y)=100(y-x^2)^2+(1-x)^2

e x t re m e f (x, y) = 100 (y - x^{2})^{2} + (1 - x)^{2}

extreme f(x)=120x-0.4x^4+1000

e x t re m e f (x) = 120 x - 0.4 x^{4} + 1000

extreme f(x)=-3/2 sin(3/2 x)

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

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

extreme f(x)=(x^2+4)(16-x^2)

e x t re m e f (x) = (x^{2} + 4) (16 - x^{2})