extreme x^2(x^2-2)

Lösung

extrempunkte

x^{2} (x^{2} - 2)

Minimum (- 1, - 1), Maximum (0, 0), Minimum (1, - 1)

Schritte zur Lösung

f^{'} (x) = 4 x (x + 1) (x - 1)

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

x^{2} (x^{2} - 2) : - 1

Minimum (- 1, - 1)

Stecke

x = 0

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

Maximum (0, 0)

Stecke

x = 1

x^{2} (x^{2} - 2) : - 1

Minimum (1, - 1)

Minimum (- 1, - 1), Maximum (0, 0), Minimum (1, - 1)

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

e x t re m e y = x^{5} - 5 x^{4}

e x t re m e f (x) = x^{3} + 3 x^{2}, - \frac{5}{2} \leq x \leq 1

e x t re m e \frac{1}{( x + 1 ) ( x + 2 ) ( x + 3 )}

e x t re m e f (x) = 3 x^{2} + 10 x - 5