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Beliebt Funktionen >

extreme f(x)=x^3(x-1)^2

Lösung

extrempunkte

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

Lösung

Sattel (0, 0), Maximum (\frac{3}{5}, \frac{108}{3125}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = x^{2} (x - 1) (5 x - 3)

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{3}{5},

Absteigend

: \frac{3}{5} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = 0

in

x^{3} (x - 1)^{2} : 0

Sattel (0, 0)

Stecke

x = \frac{3}{5}

in

x^{3} (x - 1)^{2} : \frac{108}{3125}

Maximum (\frac{3}{5}, \frac{108}{3125})

Stecke

x = 1

in

x^{3} (x - 1)^{2} : 0

Minimum (1, 0)

Sattel (0, 0), Maximum (\frac{3}{5}, \frac{108}{3125}), Minimum (1, 0)

Graph

Beliebte Beispiele

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

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

extreme f(x)=(t^2-1)^3

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

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

e x t re m e f (x) = 2 x - 4 sin (x)

extreme f(x)=x\sqrt[3]{x^2-4}

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

extreme f(x,y)=x^3+y^3-33xy

e x t re m e f (x, y) = x^{3} + y^{3} - 33 x y