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Beliebt Funktionen >

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

Lösung

extrempunkte

f (x) = \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x

Lösung

Maximum (- 2, \frac{22}{3}), Minimum (3, - \frac{27}{2})

Schritte zur Lösung

f^{'} (x) = x^{2} - x - 6

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 2

in

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : \frac{22}{3}

Maximum (- 2, \frac{22}{3})

Stecke

x = 3

in

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : - \frac{27}{2}

Minimum (3, - \frac{27}{2})

Maximum (- 2, \frac{22}{3}), Minimum (3, - \frac{27}{2})

Graph

Beliebte Beispiele

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

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

extreme f(x,y)=x^3+y^3-12xy

e x t re m e f (x, y) = x^{3} + y^{3} - 12 x y

extreme f(x,y)=2x^2+2xy+y^2+2x-3

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

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

e x t re m e f (x) = \frac{3 x + 1}{1 - 2 x}

extreme f(x,y)=16x+12y-2x^2-3y^2

e x t re m e f (x, y) = 16 x + 12 y - 2 x^{2} - 3 y^{2}