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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (1, 2 \cdot 2^{\frac{2}{3}}), Minimum (5, 0)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 1,

Absteigend

: 1 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 1

in

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

Maximum (1, 2 \cdot 2^{\frac{2}{3}})

Stecke

x = 5

in

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

Minimum (5, 0)

Maximum (1, 2 \cdot 2^{\frac{2}{3}}), Minimum (5, 0)

Graph

Beliebte Beispiele

extreme x^{1/3}(x^2-9)

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