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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{81}{16}), Minimum (3, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

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

Absteigend

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

Ansteigend

: 3 < x < \infty

Stecke

x = 0

in

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

Minimum (0, 0)

Stecke

x = \frac{3}{2}

in

x^{2} (x - 3)^{2} : \frac{81}{16}

Maximum (\frac{3}{2}, \frac{81}{16})

Stecke

x = 3

in

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

Minimum (3, 0)

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{81}{16}), Minimum (3, 0)

Graph

Beliebte Beispiele

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