extreme f(x)=2x^4-16x^2+3

Lösung

extrempunkte

f (x) = 2 x^{4} - 16 x^{2} + 3

Minimum (- 2, - 29), Maximum (0, 3), Minimum (2, - 29)

Schritte zur Lösung

f^{'} (x) = 8 x^{3} - 32 x

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

2 x^{4} - 16 x^{2} + 3 : - 29

Minimum (- 2, - 29)

Stecke

x = 0

2 x^{4} - 16 x^{2} + 3 : 3

Maximum (0, 3)

Stecke

x = 2

2 x^{4} - 16 x^{2} + 3 : - 29

Minimum (2, - 29)

Minimum (- 2, - 29), Maximum (0, 3), Minimum (2, - 29)

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

e x t re m e f (x, y) = \frac{1}{x y}

roo t s 16 x y

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

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