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Beliebt Funktionen >

extreme f(x)=x(x-10)^2

Lösung

extrempunkte

f (x) = x (x - 10)^{2}

Lösung

Maximum (\frac{10}{3}, \frac{4000}{27}), Minimum (10, 0)

Schritte zur Lösung

f^{'} (x) = (x - 10) (3 x - 10)

Intervalle finden:

Ansteigend

: - \infty < x < \frac{10}{3},

Absteigend

: \frac{10}{3} < x < 10,

Ansteigend

: 10 < x < \infty

Stecke

x = \frac{10}{3}

in

x (x - 10)^{2} : \frac{4000}{27}

Maximum (\frac{10}{3}, \frac{4000}{27})

Stecke

x = 10

in

x (x - 10)^{2} : 0

Minimum (10, 0)

Maximum (\frac{10}{3}, \frac{4000}{27}), Minimum (10, 0)

Graph

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