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Beliebt Funktionen >

extreme f(x)=3x^4+4x^3-36x^2-78

Lösung

extrempunkte

f (x) = 3 x^{4} + 4 x^{3} - 36 x^{2} - 78

Lösung

Minimum (- 3, - 267), Maximum (0, - 78), Minimum (2, - 142)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} + 12 x^{2} - 72 x

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 3

in

3 x^{4} + 4 x^{3} - 36 x^{2} - 78 : - 267

Minimum (- 3, - 267)

Stecke

x = 0

in

3 x^{4} + 4 x^{3} - 36 x^{2} - 78 : - 78

Maximum (0, - 78)

Stecke

x = 2

in

3 x^{4} + 4 x^{3} - 36 x^{2} - 78 : - 142

Minimum (2, - 142)

Minimum (- 3, - 267), Maximum (0, - 78), Minimum (2, - 142)

Graph

Beliebte Beispiele

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

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

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

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

extreme f(x)=x^4-8x^2+1

e x t re m e f (x) = x^{4} - 8 x^{2} + 1

extreme f(x,y)=4x^2+y^2-8x+6y+8

e x t re m e f (x, y) = 4 x^{2} + y^{2} - 8 x + 6 y + 8

extreme f(x)=ln(27+8x^3)

e x t re m e f (x) = ln (27 + 8 x^{3})