What is the critical ((24(3x^2+4)))/((x^2-4)^3) ?

The critical ((24(3x^2+4)))/((x^2-4)^3) is x=0

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critical ((24(3x^2+4)))/((x^2-4)^3)

critical points

\frac{( 24 ( 3 x ^{2} + 4 ) )}{( x ^{2} - 4 ) ^{3}}

x = 0

Solution steps

\frac{24 ( 3 x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = - 2, x = 2

Identify critical points not in

f (x)

domain

Domain of

\frac{24 ( 3 x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}} : x < - 2 or - 2 < x < 2 or x > 2

\frac{24 ( 3 x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

is not defined at

x = - 2, x = 2

, therefore:

x = 0

- 1000 x^{3} - 1000 x^{2} + 8000 x + 1000

f (x) = 2 x^{3} - 9 x^{2} - 24 x + 3

f (x) = 2 x^{3} - 9 x^{2} - 24 x + 1

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

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

What is the critical ((24(3x^2+4)))/((x^2-4)^3) ?
The critical ((24(3x^2+4)))/((x^2-4)^3) is x=0