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Beliebt Funktionen >

extreme f(x)= 2/3 x^3-x^2-12x+3

Lösung

extrempunkte

f (x) = \frac{2}{3} x^{3} - x^{2} - 12 x + 3

Lösung

Maximum (- 2, \frac{53}{3}), Minimum (3, - 24)

Schritte zur Lösung

f^{'} (x) = 2 x^{2} - 2 x - 12

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 2

in

\frac{2}{3} x^{3} - x^{2} - 12 x + 3 : \frac{53}{3}

Maximum (- 2, \frac{53}{3})

Stecke

x = 3

in

\frac{2}{3} x^{3} - x^{2} - 12 x + 3 : - 24

Minimum (3, - 24)

Maximum (- 2, \frac{53}{3}), Minimum (3, - 24)

Graph

Beliebte Beispiele

extreme f(x)=-x^3+3x^2+45x-7

e x t re m e f (x) = - x^{3} + 3 x^{2} + 45 x - 7

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

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

extreme f(x,y)=(x^2-2xy+y)/(3x-2y-6)

e x t re m e f (x, y) = \frac{x ^{2} - 2 x y + y}{3 x - 2 y - 6}

extreme f(x)=x^4+6x^3+12x^2+8x+10

e x t re m e f (x) = x^{4} + 6 x^{3} + 12 x^{2} + 8 x + 10

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

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