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Beliebt Funktionen >

extreme f(x)=3x^4-4x^3-12x^2+1

Lösung

extrempunkte

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 1

Lösung

Minimum (- 1, - 4), Maximum (0, 1), Minimum (2, - 31)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - 12 x^{2} - 24 x

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 1

in

3 x^{4} - 4 x^{3} - 12 x^{2} + 1 : - 4

Minimum (- 1, - 4)

Stecke

x = 0

in

3 x^{4} - 4 x^{3} - 12 x^{2} + 1 : 1

Maximum (0, 1)

Stecke

x = 2

in

3 x^{4} - 4 x^{3} - 12 x^{2} + 1 : - 31

Minimum (2, - 31)

Minimum (- 1, - 4), Maximum (0, 1), Minimum (2, - 31)

Graph

Beliebte Beispiele

extreme f(x)=x^3-3x^2-24x+2

e x t re m e f (x) = x^{3} - 3 x^{2} - 24 x + 2

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

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

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

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

extreme f(x,y)=2-sqrt(1+x+y)

e x t re m e f (x, y) = 2 - 1 + x + y

extreme f(x)=3-4sin(3x),(0,2pi)

e x t re m e f (x) = 3 - 4 sin (3 x), (0, 2 π)