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

Lösung

extrempunkte

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

Minimum (- 2, - 18), Maximum (0, - 2), Minimum (2, - 18)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 16 x

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

x^{4} - 8 x^{2} - 2 : - 18

Minimum (- 2, - 18)

Stecke

x = 0

x^{4} - 8 x^{2} - 2 : - 2

Maximum (0, - 2)

Stecke

x = 2

x^{4} - 8 x^{2} - 2 : - 18

Minimum (2, - 18)

Minimum (- 2, - 18), Maximum (0, - 2), Minimum (2, - 18)

e x t re m e f (x) = - 2 x^{3} + 9 x^{2} - 10 x + 3

e x t re m e \frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 2 x^{2} + 4 x + 3

e x t re m e f (x, y) = 4 x y - x^{2} - y^{2} - 14 x + 4 y + 10

e x t re m e y = \frac{sin ( x )}{x} {- 2, π \leq x \leq 2 π}

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