extreme x^3+2x^2-4x+2

Lösung

extrempunkte

x^{3} + 2 x^{2} - 4 x + 2

Maximum (- 2, 10), Minimum (\frac{2}{3}, \frac{14}{27})

Schritte zur Lösung

f^{'} (x) = 3 x^{2} + 4 x - 4

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < \frac{2}{3},

Ansteigend

: \frac{2}{3} < x < \infty

Stecke

x = - 2

x^{3} + 2 x^{2} - 4 x + 2 : 10

Maximum (- 2, 10)

Stecke

x = \frac{2}{3}

x^{3} + 2 x^{2} - 4 x + 2 : \frac{14}{27}

Minimum (\frac{2}{3}, \frac{14}{27})

Maximum (- 2, 10), Minimum (\frac{2}{3}, \frac{14}{27})

e x t re m e x^{3} + 2 x^{2} - 4 x + 8

e x t re m e f (x) = x^{3} - x^{2} - 8 x + 2

e x t re m e f (x) = x^{3} - x^{2} - 8 x + 1

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

e x t re m e f (x) = x^{3} - x^{2} - 8 x - 2