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

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

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

critical points

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

x = - \frac{3}{2}, x = 0

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{3}{2}, x = 0, x = - 1

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = - 1

, therefore:

x = - \frac{3}{2}, x = 0

f (x) = x - 2 - 3 x^{2}

f (x) = \frac{( x ^{2} + 4 x - 5 )}{( x ^{2} + x - 2 )}

- x^{2} + 4 x

f (x) = \frac{7 - 5 x}{5 x + 2}

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

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