extreme f(x)=x^4-72x^2+7

Lösung

extrempunkte

f (x) = x^{4} - 72 x^{2} + 7

Minimum (- 6, - 1289), Maximum (0, 7), Minimum (6, - 1289)

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} + 7 : - 1289

Minimum (- 6, - 1289)

Stecke

x = 0

x^{4} - 72 x^{2} + 7 : 7

Maximum (0, 7)

Stecke

x = 6

x^{4} - 72 x^{2} + 7 : - 1289

Minimum (6, - 1289)

Minimum (- 6, - 1289), Maximum (0, 7), Minimum (6, - 1289)

e x t re m e f (x, y) = x^{2} + 6 x + y^{3} - 6 y^{2} + 10

e x t re m e f (x) = 4 x + 324 x, 0 < x < \infty

e x t re m e f (x) = 2 x^{4} + 3 x^{3} - 7 x^{2} - 2 x - 24

e x t re m e f (x) = x^{2} - 9, - \frac{9}{2} \leq x \leq 6

e x t re m e x^{2} e^{- 6 x}