What is the critical f(x)=((x^3))/(x^2-1) ?

The critical f(x)=((x^3))/(x^2-1) is x=-sqrt(3),x=0,x=sqrt(3)

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critical f(x)=((x^3))/(x^2-1)

critical points

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

x = - 3, x = 0, x = 3

Solution steps

\frac{x ^{3}}{x ^{2} - 1}

Find where

f^{'} (x)

is equal to zero or undefined

x = - 3, x = 0, x = 3, x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{x ^{3}}{x ^{2} - 1} : x < - 1 or - 1 < x < 1 or x > 1

\frac{x ^{3}}{x ^{2} - 1}

is not defined at

x = - 1, x = 1

, therefore:

x = - 3, x = 0, x = 3

\frac{x ^{2} - 25}{- 2 x ^{2} - 10 x}

\frac{- 1}{x ^{2} - 2 x + 1}

\frac{5 - 2 x}{6 x + 3}

y = lo g_{a} (x)

f (x) = 5 x + 1

What is the critical f(x)=((x^3))/(x^2-1) ?
The critical f(x)=((x^3))/(x^2-1) is x=-sqrt(3),x=0,x=sqrt(3)