extreme f(x)=(x^2-1)^{2/3}

Lösung

extrempunkte

f (x) = (x^{2} - 1)^{\frac{2}{3}}

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = \frac{4 x}{3 ( x ^{2} - 1 ) ^{\frac{1}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

(x^{2} - 1)^{\frac{2}{3}} : 0

Minimum (- 1, 0)

Stecke

x = 0

(x^{2} - 1)^{\frac{2}{3}} : 1

Maximum (0, 1)

Stecke

x = 1

(x^{2} - 1)^{\frac{2}{3}} : 0

Minimum (1, 0)

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

in v erse \frac{( 2 x - 1 )}{2 x + 5}

s l o p e in t erce pt 2 x - y = 5

d o main f (x) = \frac{x + 1}{x ^{2} - 4 x - 12}

d o main f (x) = 9 + \frac{6}{x}

e x t re m e f (x) = x^{3} + 12 x + 5