extreme 2x^4-12x^2

Lösung

extrempunkte

2 x^{4} - 12 x^{2}

Minimum (- 3, - 18), Maximum (0, 0), Minimum (3, - 18)

Schritte zur Lösung

f^{'} (x) = 8 x^{3} - 24 x

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

2 x^{4} - 12 x^{2} : - 18

Minimum (- 3, - 18)

Stecke

x = 0

2 x^{4} - 12 x^{2} : 0

Maximum (0, 0)

Stecke

x = 3

2 x^{4} - 12 x^{2} : - 18

Minimum (3, - 18)

Minimum (- 3, - 18), Maximum (0, 0), Minimum (3, - 18)

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

e x t re m e f (x) = \frac{x + 5}{x ^{2} - x - 30}

e x t re m e f (x) = - x^{2} + 9, - 4 \leq x \leq 3

e x t re m e f (x, y) = \frac{x ^{3} + 9}{x ^{2}}

e x t re m e f (x) = x^{2} + 10 x y + y^{2}