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Beliebt Funktionen >

extreme f(x)=x^4+4x^3-2x^2-12x

Lösung

extrempunkte

f (x) = x^{4} + 4 x^{3} - 2 x^{2} - 12 x

Lösung

Minimum (- 3, - 9), Maximum (- 1, 7), Minimum (1, - 9)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} + 12 x^{2} - 4 x - 12

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < - 1,

Absteigend

: - 1 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 3

in

x^{4} + 4 x^{3} - 2 x^{2} - 12 x : - 9

Minimum (- 3, - 9)

Stecke

x = - 1

in

x^{4} + 4 x^{3} - 2 x^{2} - 12 x : 7

Maximum (- 1, 7)

Stecke

x = 1

in

x^{4} + 4 x^{3} - 2 x^{2} - 12 x : - 9

Minimum (1, - 9)

Minimum (- 3, - 9), Maximum (- 1, 7), Minimum (1, - 9)

Graph

Beliebte Beispiele

extreme f(x)=x^3-6x^2+10

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

extreme f(x,y)=3+sqrt(1-((x-2)^2)/4-((y-3)^2)/9)

e x t re m e f (x, y) = 3 + 1 - \frac{( x - 2 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{9}

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

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

extreme y=x^4-4x^3

e x t re m e y = x^{4} - 4 x^{3}

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

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