extreme x^3-3x^2-9x+9

Lösung

extrempunkte

x^{3} - 3 x^{2} - 9 x + 9

Maximum (- 1, 14), Minimum (3, - 18)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 6 x - 9

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 1

x^{3} - 3 x^{2} - 9 x + 9 : 14

Maximum (- 1, 14)

Stecke

x = 3

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

Minimum (3, - 18)

Maximum (- 1, 14), Minimum (3, - 18)

e x t re m e f (x) = x (x - 9)^{2}

e x t re m e f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 60

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

e x t re m e y (t, β) = - 4 e^{- 4 t} (β + 15) + 5 e^{- 5 t} (β + 12)

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