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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 1

in

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

Minimum (- 1, - \frac{3}{2})

Stecke

x = 2

in

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

Maximum (2, 3)

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

Graph

Beliebte Beispiele

extreme y=x^2-12x+1

e x t re m e y = x^{2} - 12 x + 1

extreme (-4)/(x^3)+(30)/((10x+3)^2)

e x t re m e \frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}}

extreme (x-2)^3

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

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

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

extreme f(x)=x^{8/9}-3

e x t re m e f (x) = x^{\frac{8}{9}} - 3