extreme x^4-2x^2+1

Lösung

extrempunkte

x^{4} - 2 x^{2} + 1

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

x^{4} - 2 x^{2} + 1 : 0

Minimum (- 1, 0)

Stecke

x = 0

x^{4} - 2 x^{2} + 1 : 1

Maximum (0, 1)

Stecke

x = 1

x^{4} - 2 x^{2} + 1 : 0

Minimum (1, 0)

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

e x t re m e y = 63 x + 12 cos (x)

e x t re m e f (x, y) = x^{2} + 7 y^{2} + x - 6 y + 4

e x t re m e f (x) = 2 x^{2} ln (x) - 19 x^{2}

e x t re m e f (x, y) = x^{2} + 9 x y + y^{2}

e x t re m e f (x) = x^{4} - 12 x^{3} + 4