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Beliebt Funktionen >

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

Lösung

extrempunkte

f (x) = (1 - x^{2})^{2}

Lösung

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

Schritte zur Lösung

f^{'} (x) = - 4 x (1 - x^{2})

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

in

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

Minimum (- 1, 0)

Stecke

x = 0

in

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

Maximum (0, 1)

Stecke

x = 1

in

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

Minimum (1, 0)

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

Graph

Beliebte Beispiele

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

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

extreme f(x)=ln(x^2+x+1)

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

extreme f(x)=x^2-4xy+y^3+4y

e x t re m e f (x) = x^{2} - 4 x y + y^{3} + 4 y

solvefor V,V=13pir2h

so l v e f or V, V = 13 π r 2 h

extreme f(x)=x^3+3xy+y^3

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