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

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

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

critical points

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

x = 0

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = - 1, x = 1

, therefore:

x = 0

f (x) = 9 x + 9 x^{- 1}

\frac{4 e ^{4 x}}{3 x - 15}

2 x^{3} - 15 x^{2} + y^{3} + 6 y^{2}

- 7 (x + 3)^{2} (x - 1) (x - 5)

f (x) = \frac{( 5 x ^{2} )}{x ^{2} + 16}

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