extreme x^4-32x^2

Lösung

extrempunkte

x^{4} - 32 x^{2}

Minimum (- 4, - 256), Maximum (0, 0), Minimum (4, - 256)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 64 x

Intervalle finden:

Absteigend

: - \infty < x < - 4,

Ansteigend

: - 4 < x < 0,

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - 4

x^{4} - 32 x^{2} : - 256

Minimum (- 4, - 256)

Stecke

x = 0

x^{4} - 32 x^{2} : 0

Maximum (0, 0)

Stecke

x = 4

x^{4} - 32 x^{2} : - 256

Minimum (4, - 256)

Minimum (- 4, - 256), Maximum (0, 0), Minimum (4, - 256)

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

e x t re m e f (x) = 3 x^{4} - 4 x^{3} - 8, - 1 \leq x \leq 2

e x t re m e K (y, z) = 3 yz

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

e x t re m e f (x) = \frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23