What is the critical 1/(x^3-x) ?

The critical 1/(x^3-x) is x=-1/(sqrt(3)),x= 1/(sqrt(3))

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critical 1/(x^3-x)

critical points

\frac{1}{x ^{3} - x}

x = - \frac{1}{3}, x = \frac{1}{3}

Solution steps

\frac{1}{x ^{3} - x}

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{1}{3}, x = \frac{1}{3}, x = - 1, x = 0, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{1}{x ^{3} - x} : x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

\frac{1}{x ^{3} - x}

is not defined at

x = - 1, x = 0, x = 1

, therefore:

x = - \frac{1}{3}, x = \frac{1}{3}

x^{3} + x^{2} - 8 x + 5

f (x, y) = x y + ln (x) + 32 y^{2}

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

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

f (x) = 5 x^{3} - 3 x^{5}

What is the critical 1/(x^3-x) ?
The critical 1/(x^3-x) is x=-1/(sqrt(3)),x= 1/(sqrt(3))