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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (- 2, 0), Minimum (\frac{2}{3}, - \frac{4 \cdot 4 ^{\frac{1}{3}}}{3})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

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

Ansteigend

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

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

in

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

Maximum (- 2, 0)

Stecke

x = \frac{2}{3}

in

(x + 2)^{\frac{2}{3}} (x - 2)^{\frac{1}{3}} : - \frac{4 \cdot 4 ^{\frac{1}{3}}}{3}

Minimum (\frac{2}{3}, - \frac{4 \cdot 4 ^{\frac{1}{3}}}{3})

Maximum (- 2, 0), Minimum (\frac{2}{3}, - \frac{4 \cdot 4 ^{\frac{1}{3}}}{3})

Graph

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