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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (0, 1), Minimum (\frac{2}{3}, - \frac{4}{27} + 1)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

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

Ansteigend

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

Stecke

x = 0

in

x^{3} - x^{2} + 1 : 1

Maximum (0, 1)

Stecke

x = \frac{2}{3}

in

x^{3} - x^{2} + 1 : - \frac{4}{27} + 1

Minimum (\frac{2}{3}, - \frac{4}{27} + 1)

Maximum (0, 1), Minimum (\frac{2}{3}, - \frac{4}{27} + 1)

Graph

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