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Beliebt Funktionen >

extreme f(x)=x^4-2x^2+8

Lösung

extrempunkte

f (x) = x^{4} - 2 x^{2} + 8

Lösung

Minimum (- 1, 7), Maximum (0, 8), Minimum (1, 7)

Schritte zur Lösung

f^{'} (x) = 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

in

x^{4} - 2 x^{2} + 8 : 7

Minimum (- 1, 7)

Stecke

x = 0

in

x^{4} - 2 x^{2} + 8 : 8

Maximum (0, 8)

Stecke

x = 1

in

x^{4} - 2 x^{2} + 8 : 7

Minimum (1, 7)

Minimum (- 1, 7), Maximum (0, 8), Minimum (1, 7)

Graph

Beliebte Beispiele

extreme f(x)=-1/(x-2)

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

extreme f(x)=(8-(\sqrt[3]{x^2+2x+1}))

e x t re m e f (x) = (8 - (3 x^{2} + 2 x + 1))

extreme f(x)=((2x^2))/(9-x^2)

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

extreme f(x)=-1/(x-6)

e x t re m e f (x) = - \frac{1}{x - 6}

extreme f(x,y)=18x^2-3y^2-36x-128y-110

e x t re m e f (x, y) = 18 x^{2} - 3 y^{2} - 36 x - 128 y - 110