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Beliebt Funktionen >

extreme f(x)= 1/4 x^4+1/3 x^3-x^2+2

Lösung

extrempunkte

f (x) = \frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + 2

Lösung

Minimum (- 2, - \frac{2}{3}), Maximum (0, 2), Minimum (1, \frac{19}{12})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

in

\frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + 2 : - \frac{2}{3}

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

Stecke

x = 0

in

\frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + 2 : 2

Maximum (0, 2)

Stecke

x = 1

in

\frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + 2 : \frac{19}{12}

Minimum (1, \frac{19}{12})

Minimum (- 2, - \frac{2}{3}), Maximum (0, 2), Minimum (1, \frac{19}{12})

Graph

Beliebte Beispiele

extreme f(x,y)=x^2+2y^2-2x-4y+1

e x t re m e f (x, y) = x^{2} + 2 y^{2} - 2 x - 4 y + 1

extreme f(x,y)=2x^2+y^2+8x-6y-2xy+12

e x t re m e f (x, y) = 2 x^{2} + y^{2} + 8 x - 6 y - 2 x y + 12

extreme f(x)=x^3-3x^2+24x

e x t re m e f (x) = x^{3} - 3 x^{2} + 24 x

extreme f(x)=(2x)/(x-1)

e x t re m e f (x) = \frac{2 x}{x - 1}

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

e x t re m e f (x) = \frac{x ^{2}}{x + 4}