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Beliebt Funktionen >

extreme f(x)=x^{2/3}(20-3x)

Lösung

extrempunkte

f (x) = x^{\frac{2}{3}} (20 - 3 x)

Lösung

Minimum (0, 0), Maximum (\frac{8}{3}, 16 \cdot 3^{\frac{1}{3}})

Schritte zur Lösung

f^{'} (x) = - \frac{5 ( 3 x - 8 )}{3 x ^{\frac{1}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{8}{3},

Absteigend

: \frac{8}{3} < x < \infty

Stecke

x = 0

in

x^{\frac{2}{3}} (20 - 3 x) : 0

Minimum (0, 0)

Stecke

x = \frac{8}{3}

in

x^{\frac{2}{3}} (20 - 3 x) : 16 \cdot 3^{\frac{1}{3}}

Maximum (\frac{8}{3}, 16 \cdot 3^{\frac{1}{3}})

Minimum (0, 0), Maximum (\frac{8}{3}, 16 \cdot 3^{\frac{1}{3}})

Graph

Beliebte Beispiele

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