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

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

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

critical points

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

x = 0, x = 2

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = 2, x = 1

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = 1

, therefore:

x = 0, x = 2

f (x) = 4 x^{3} + 3 x^{2} - 6 x

f (x) = 6 x^{5} - 90 x^{3}

f (x) = 5 x^{\frac{2}{3}} + x^{\frac{5}{3}}

x^{2} e^{- 2 x}

\frac{x + 2}{x - 4} + 2

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