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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

f^{'} (x) = 4 x (x + 1) (x - 1)

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

in

x^{2} (x^{2} - 2) : - 1

Minimum (- 1, - 1)

Stecke

x = 0

in

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

Maximum (0, 0)

Stecke

x = 1

in

x^{2} (x^{2} - 2) : - 1

Minimum (1, - 1)

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

Graph

Beliebte Beispiele

extreme f(x)=x^2-9,-4<= x<= 3

e x t re m e f (x) = x^{2} - 9, - 4 \leq x \leq 3

extreme f(x,y)=x^2y-15xy^2+12y

e x t re m e f (x, y) = x^{2} y - 15 x y^{2} + 12 y

extreme f(x,y)=3x^2y-3x^2-3y^2+y^3+2

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

extreme y=x^3-3x+7

e x t re m e y = x^{3} - 3 x + 7

extreme x^4-x^3-6x^2

e x t re m e x^{4} - x^{3} - 6 x^{2}