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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (- 1, 0), Maximum (0, \frac{3}{5}), Minimum (1, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

in

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

Minimum (- 1, 0)

Stecke

x = 0

in

\frac{3}{5} (x^{2} - 1)^{\frac{2}{3}} : \frac{3}{5}

Maximum (0, \frac{3}{5})

Stecke

x = 1

in

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

Minimum (1, 0)

Minimum (- 1, 0), Maximum (0, \frac{3}{5}), Minimum (1, 0)

Graph

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