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Beliebt Funktionen >

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

Lösung

extrempunkte

f (x) = x^{4} + \frac{4 x ^{3}}{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 x ^{3}}{3} - 4 x^{2} : - \frac{32}{3}

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

Stecke

x = 0

in

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

Maximum (0, 0)

Stecke

x = 1

in

x^{4} + \frac{4 x ^{3}}{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)=3y^2-2y^3-3x^2+6xy

e x t re m e f (x) = 3 y^{2} - 2 y^{3} - 3 x^{2} + 6 x y

extreme f(x)=3x^3-6x^2-5x+1

e x t re m e f (x) = 3 x^{3} - 6 x^{2} - 5 x + 1

extreme f(x,y)=8x^3-24xy+y^3

e x t re m e f (x, y) = 8 x^{3} - 24 x y + y^{3}

extreme f(x)=e^{x^2}

e x t re m e f (x) = e^{x^{2}}

extreme f(x)=x^3-12x^2+45x+8

e x t re m e f (x) = x^{3} - 12 x^{2} + 45 x + 8