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Beliebt Funktionen >

extreme f(x)=(x^2-3)^2

Lösung

extrempunkte

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

Lösung

Minimum (- 3, 0), Maximum (0, 9), Minimum (3, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

in

(x^{2} - 3)^{2} : 0

Minimum (- 3, 0)

Stecke

x = 0

in

(x^{2} - 3)^{2} : 9

Maximum (0, 9)

Stecke

x = 3

in

(x^{2} - 3)^{2} : 0

Minimum (3, 0)

Minimum (- 3, 0), Maximum (0, 9), Minimum (3, 0)

Graph

Beliebte Beispiele

extreme f(x)=(x-1)e^x

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

extreme (x^2+1)/(x^2-4)

e x t re m e \frac{x ^{2} + 1}{x ^{2} - 4}

extreme f(x,y)=-x^2-y^2+8x+6y

e x t re m e f (x, y) = - x^{2} - y^{2} + 8 x + 6 y

extreme f(x)=x+e^{-2x}

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

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

e x t re m e f (x) = - x (x + 2) (x - 2)