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Beliebt Funktionen >

extreme f(x)=x^4+4/3 x^3-4x^2

Lösung

extrempunkte

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

Lösung

Minimum (- 2, - \frac{32}{3}), Maximum (0, 0), Minimum (1, - \frac{5}{3})

Schritte zur Lösung

f^{'} (x) = 4 x^{3} + 4 x^{2} - 8 x

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

in

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} : - \frac{32}{3}

Minimum (- 2, - \frac{32}{3})

Stecke

x = 0

in

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} : 0

Maximum (0, 0)

Stecke

x = 1

in

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} : - \frac{5}{3}

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

Minimum (- 2, - \frac{32}{3}), Maximum (0, 0), Minimum (1, - \frac{5}{3})

Graph

Beliebte Beispiele

extreme f(x)=sin(x)cos(x)

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e x t re m e f (x, y) = x^{3} + y^{3} - 6 x y

extreme f(x,y)=1-x^2-y^2

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