extreme f(x)=x^4-72x^2

Lösung

extrempunkte

f (x) = x^{4} - 72 x^{2}

Minimum (- 6, - 1296), Maximum (0, 0), Minimum (6, - 1296)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 144 x

Intervalle finden:

Absteigend

: - \infty < x < - 6,

Ansteigend

: - 6 < x < 0,

Absteigend

: 0 < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = - 6

x^{4} - 72 x^{2} : - 1296

Minimum (- 6, - 1296)

Stecke

x = 0

x^{4} - 72 x^{2} : 0

Maximum (0, 0)

Stecke

x = 6

x^{4} - 72 x^{2} : - 1296

Minimum (6, - 1296)

Minimum (- 6, - 1296), Maximum (0, 0), Minimum (6, - 1296)

e x t re m e f (x) = - 3 x^{4} ln (3 x), (0, 4)

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

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

e x t re m e 2 x^{2} y - 4 y^{2} - 8 y - 4

e x t re m e f (x) = (x + 1)^{3} (x - 1)