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

Lösung

extrempunkte

f (x) = x^{4} - 6 x^{2} + 8 x

Minimum (- 2, - 24), Sattel (1, 3)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 12 x + 8

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

x^{4} - 6 x^{2} + 8 x : - 24

Minimum (- 2, - 24)

Stecke

x = 1

x^{4} - 6 x^{2} + 8 x : 3

Sattel (1, 3)

Minimum (- 2, - 24), Sattel (1, 3)

e x t re m e f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{4} - 5 x + 5

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

e x t re m e f (x, y) = x^{2} - 4 x y + 5 y^{2} + 2 x + 4 y - 4

e x t re m e f (x) = 1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}}

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