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Beliebt Funktionen >

extreme f(x)=x^4(x-1)^2

Lösung

extrempunkte

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

Lösung

Minimum (0, 0), Maximum (\frac{2}{3}, \frac{16}{729}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = 2 x^{3} (x - 1) (3 x - 2)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{2}{3},

Absteigend

: \frac{2}{3} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = 0

in

x^{4} (x - 1)^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{2}{3}

in

x^{4} (x - 1)^{2} : \frac{16}{729}

Maximum (\frac{2}{3}, \frac{16}{729})

Stecke

x = 1

in

x^{4} (x - 1)^{2} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{2}{3}, \frac{16}{729}), Minimum (1, 0)

Graph

Beliebte Beispiele

extreme (4x^2-3x^4)/(2x)

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

extreme f(x)=(2e^{3x})/(-3x-1)

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

extreme f(x)=-5x^6ln(x)

e x t re m e f (x) = - 5 x^{6} ln (x)

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

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

extreme f(x)=(x^2-16x+64)/(x-10)

e x t re m e f (x) = \frac{x ^{2} - 16 x + 64}{x - 10}