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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 0

in

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

Maximum (0, 3)

Stecke

x = 2

in

\frac{1}{3} x^{3} - x^{2} + 3 : \frac{5}{3}

Minimum (2, \frac{5}{3})

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

Graph

Beliebte Beispiele

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

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

extreme (x+2)^2(x-3)

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

extreme f(x)=3cos(2x)+4

e x t re m e f (x) = 3 cos (2 x) + 4

extreme f(x)=3x+6x^{-1}

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

extreme f(x,y)=-x^3+y^3+15xy+1

e x t re m e f (x, y) = - x^{3} + y^{3} + 15 x y + 1