extreme f(x)=(x+1)^3(x-1)

Lösung

extrempunkte

f (x) = (x + 1)^{3} (x - 1)

Sattel (- 1, 0), Minimum (\frac{1}{2}, - \frac{27}{16})

Schritte zur Lösung

f^{'} (x) = 2 (x + 1)^{2} (2 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < \frac{1}{2},

Ansteigend

: \frac{1}{2} < x < \infty

Stecke

x = - 1

(x + 1)^{3} (x - 1) : 0

Sattel (- 1, 0)

Stecke

x = \frac{1}{2}

(x + 1)^{3} (x - 1) : - \frac{27}{16}

Minimum (\frac{1}{2}, - \frac{27}{16})

Sattel (- 1, 0), Minimum (\frac{1}{2}, - \frac{27}{16})

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

e x t re m e f (x) = 14 x^{3} + 336 x^{2}

e x t re m e f (x) = x^{2} + \frac{14}{x}

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

e x t re m e f (x) = x^{\frac{1}{3}} (x - 7)^{2}