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Beliebt Funktionen >

extreme f(x)= 1/5 x^5-1/4 x^4-2x^3

Lösung

extrempunkte

f (x) = \frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3}

Lösung

Maximum (- 2, \frac{28}{5}), Sattel (0, 0), Minimum (3, - \frac{513}{20})

Schritte zur Lösung

f^{'} (x) = x^{4} - x^{3} - 6 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 2

in

\frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3} : \frac{28}{5}

Maximum (- 2, \frac{28}{5})

Stecke

x = 0

in

\frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3} : 0

Sattel (0, 0)

Stecke

x = 3

in

\frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3} : - \frac{513}{20}

Minimum (3, - \frac{513}{20})

Maximum (- 2, \frac{28}{5}), Sattel (0, 0), Minimum (3, - \frac{513}{20})

Graph

Beliebte Beispiele

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