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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (0, 0), Maximum (\frac{4}{3}, \frac{32}{27})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{4}{3},

Absteigend

: \frac{4}{3} < x < \infty

Stecke

x = 0

in

- x^{3} + 2 x^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{4}{3}

in

- x^{3} + 2 x^{2} : \frac{32}{27}

Maximum (\frac{4}{3}, \frac{32}{27})

Minimum (0, 0), Maximum (\frac{4}{3}, \frac{32}{27})

Graph

Beliebte Beispiele

extreme f(x,y)=x^y

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

extreme f(x)=4x^3-39x^2+90x+2

e x t re m e f (x) = 4 x^{3} - 39 x^{2} + 90 x + 2

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

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

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

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

extreme f(x)=cos(3x)

e x t re m e f (x) = cos (3 x)