extreme f(x)=-x^3-9x^2-24x+2

Lösung

extrempunkte

f (x) = - x^{3} - 9 x^{2} - 24 x + 2

Minimum (- 4, 18), Maximum (- 2, 22)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} - 18 x - 24

Intervalle finden:

Absteigend

: - \infty < x < - 4,

Ansteigend

: - 4 < x < - 2,

Absteigend

: - 2 < x < \infty

Stecke

x = - 4

- x^{3} - 9 x^{2} - 24 x + 2 : 18

Minimum (- 4, 18)

Stecke

x = - 2

- x^{3} - 9 x^{2} - 24 x + 2 : 22

Maximum (- 2, 22)

Minimum (- 4, 18), Maximum (- 2, 22)

e x t re m e f (x) = x^{2} + y^{2} + 5

e x t re m e f (x, y) = 5 x^{2} - 4 x y + y^{2} - 16 x - 12 y - 4

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

e x t re m e f (x) = \frac{2}{3} x^{3} - 6 x^{2} + 16 x

e x t re m e f (x, y) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y