extreme y=x^4-18x^2

Lösung

extrempunkte

y = x^{4} - 18 x^{2}

Minimum (- 3, - 81), Maximum (0, 0), Minimum (3, - 81)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 36 x

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

x^{4} - 18 x^{2} : - 81

Minimum (- 3, - 81)

Stecke

x = 0

x^{4} - 18 x^{2} : 0

Maximum (0, 0)

Stecke

x = 3

x^{4} - 18 x^{2} : - 81

Minimum (3, - 81)

Minimum (- 3, - 81), Maximum (0, 0), Minimum (3, - 81)

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

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

e x t re m e f (x) = 2 x^{2} - 4 x

e x t re m e f (x) = \frac{1}{2} y^{4} - 4 x y + 2 x^{4}

e x t re m e f (x, y) = 338 y^{2} + x^{2} - x^{2} y