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Beliebt Funktionen >

extreme f(x)=3x^4-4x^3-12x^2-7

Lösung

extrempunkte

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} - 7

Lösung

Minimum (- 1, - 12), Maximum (0, - 7), Minimum (2, - 39)

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} - 7 : - 12

Minimum (- 1, - 12)

Stecke

x = 0

in

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

Maximum (0, - 7)

Stecke

x = 2

in

3 x^{4} - 4 x^{3} - 12 x^{2} - 7 : - 39

Minimum (2, - 39)

Minimum (- 1, - 12), Maximum (0, - 7), Minimum (2, - 39)

Graph

Beliebte Beispiele

extreme f(x,y)=e^y(4x^2+2xy+y^2-6x-15)

e x t re m e f (x, y) = e^{y} (4 x^{2} + 2 x y + y^{2} - 6 x - 15)

extreme 2(x-1)^2+5

e x t re m e 2 (x - 1)^{2} + 5

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

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

extreme-4sin(2pix)

e x t re m e - 4 sin (2 π x)

extreme f(x)=20+8x^3-x^4

e x t re m e f (x) = 20 + 8 x^{3} - x^{4}