extreme y=x^3-3x^2-9x

Lösung

extrempunkte

y = x^{3} - 3 x^{2} - 9 x

Maximum (- 1, 5), Minimum (3, - 27)

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 : 5

Maximum (- 1, 5)

Stecke

x = 3

x^{3} - 3 x^{2} - 9 x : - 27

Minimum (3, - 27)

Maximum (- 1, 5), Minimum (3, - 27)

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

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

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

e x t re m e f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

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