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Beliebt Funktionen >

extreme f(x)=x^{4/3}(7x^2+10x-210)

Lösung

extrempunkte

f (x) = x^{\frac{4}{3}} (7 x^{2} + 10 x - 210)

Lösung

Minimum (- 4, - 552 \cdot 4^{\frac{1}{3}}), Maximum (0, 0), Minimum (3, - 351 \cdot 3^{\frac{1}{3}})

Schritte zur Lösung

f^{'} (x) = \frac{70 x ^{\frac{1}{3}} ( x - 3 ) ( x + 4 )}{3}

Intervalle finden:

Absteigend

: - \infty < x < - 4,

Ansteigend

: - 4 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 4

in

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210) : - 552 \cdot 4^{\frac{1}{3}}

Minimum (- 4, - 552 \cdot 4^{\frac{1}{3}})

Stecke

x = 0

in

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210) : 0

Maximum (0, 0)

Stecke

x = 3

in

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210) : - 351 \cdot 3^{\frac{1}{3}}

Minimum (3, - 351 \cdot 3^{\frac{1}{3}})

Minimum (- 4, - 552 \cdot 4^{\frac{1}{3}}), Maximum (0, 0), Minimum (3, - 351 \cdot 3^{\frac{1}{3}})

Graph

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