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

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

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

critical points

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

x = - 3, x = 0, x = 3

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = - 3, x = 0, x = 3, x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = - 1, x = 1

, therefore:

x = - 3, x = 0, x = 3

x^{2} + 3 x + 1

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

f (x) = x^{3} - 1

x - 2 y = 2

y = 2 x + 7

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