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Beliebt Funktionen >

extreme x^2(1-x)^3

Lösung

extrempunkte

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

Lösung

Minimum (0, 0), Maximum (\frac{2}{5}, \frac{108}{3125}), Sattel (1, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{2}{5},

Absteigend

: \frac{2}{5} < x < 1,

Absteigend

: 1 < x < \infty

Stecke

x = 0

in

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

Minimum (0, 0)

Stecke

x = \frac{2}{5}

in

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

Maximum (\frac{2}{5}, \frac{108}{3125})

Stecke

x = 1

in

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

Sattel (1, 0)

Minimum (0, 0), Maximum (\frac{2}{5}, \frac{108}{3125}), Sattel (1, 0)

Graph

Beliebte Beispiele

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e x t re m e p (x) = 3 x^{3} - 13 x^{2} + a x - 8

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e x t re m e o

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