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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Sattel (0, 12), Minimum (3, - 15)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = 0

in

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

Sattel (0, 12)

Stecke

x = 3

in

x^{4} - 4 x^{3} + 12 : - 15

Minimum (3, - 15)

Sattel (0, 12), Minimum (3, - 15)

Graph

Beliebte Beispiele

extreme f(x)=4x^3+48x^2+180x

e x t re m e f (x) = 4 x^{3} + 48 x^{2} + 180 x

extreme f(x)=x^3-x^2-8x+4

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

extreme f(x)=x^3-x^2-8x+8

e x t re m e f (x) = x^{3} - x^{2} - 8 x + 8

extreme f(x,y)=x^3+y^3-24xy

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

extreme f(x)= 8/x+2pix^2

e x t re m e f (x) = \frac{8}{x} + 2 π x^{2}