What is the critical f(x)=(x^2)/((x^3+8)) ?

The critical f(x)=(x^2)/((x^3+8)) is x=0,x=2\sqrt[3]{2}

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critical f(x)=(x^2)/((x^3+8))

critical points

f (x) = \frac{x ^{2}}{( x ^{3} + 8 )}

Solution steps

\frac{x ^{2}}{x ^{3} + 8}

Find where

f^{'} (x)

is equal to zero or undefined

Identify critical points not in

f (x)

domain

Domain of

\frac{x ^{2}}{x ^{3} + 8} : x < - 2 or x > - 2

\frac{x ^{2}}{x ^{3} + 8}

is not defined at

x = - 2

, therefore:

What is the critical f(x)=(x^2)/((x^3+8)) ?
The critical f(x)=(x^2)/((x^3+8)) is x=0,x=2\sqrt[3]{2}