extreme y=(x^2-9)^4

Lösung

extrempunkte

y = (x^{2} - 9)^{4}

Minimum (- 3, 0), Maximum (0, 6561), Minimum (3, 0)

Schritte zur Lösung

f^{'} (x) = 8 x (x^{2} - 9)^{3}

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

(x^{2} - 9)^{4} : 0

Minimum (- 3, 0)

Stecke

x = 0

(x^{2} - 9)^{4} : 6561

Maximum (0, 6561)

Stecke

x = 3

(x^{2} - 9)^{4} : 0

Minimum (3, 0)

Minimum (- 3, 0), Maximum (0, 6561), Minimum (3, 0)

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

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

e x t re m e f (x) = x^{2} + 10 + 24

e x t re m e f (x, y) = ln 4 x^{2} + 18 y^{2} - 36

e x t re m e f (x, y) = x^{2} + 2 x y + 2 y^{2} - 6 x + 10 y + 2