extreme 2x^4-196x^2-3

Lösung

extrempunkte

2 x^{4} - 196 x^{2} - 3

Minimum (- 7, - 4805), Maximum (0, - 3), Minimum (7, - 4805)

Schritte zur Lösung

f^{'} (x) = 8 x^{3} - 392 x

Intervalle finden:

Absteigend

: - \infty < x < - 7,

Ansteigend

: - 7 < x < 0,

Absteigend

: 0 < x < 7,

Ansteigend

: 7 < x < \infty

Stecke

x = - 7

2 x^{4} - 196 x^{2} - 3 : - 4805

Minimum (- 7, - 4805)

Stecke

x = 0

2 x^{4} - 196 x^{2} - 3 : - 3

Maximum (0, - 3)

Stecke

x = 7

2 x^{4} - 196 x^{2} - 3 : - 4805

Minimum (7, - 4805)

Minimum (- 7, - 4805), Maximum (0, - 3), Minimum (7, - 4805)

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

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

e x t re m e f (t) = 4 t^{3} - 36 t^{2} + 10, t \geq 0

e x t re m e f (x) = 3 x^{4} + 20 x^{3} - 36 x^{2} - 4

e x t re m e 2 x^{3} - 30 x^{2}, - 1 \leq x \leq 11