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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

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

Absteigend

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

Ansteigend

: 1 < x < \infty

Stecke

x = 0

in

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

Minimum (0, 0)

Stecke

x = \frac{1}{2}

in

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

Maximum (\frac{1}{2}, \frac{1}{16})

Stecke

x = 1

in

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

Minimum (1, 0)

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

Graph

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