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

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

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

critical points

y = \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

f (x) = 3 t^{4} + 4 t^{3} - 6 t^{2}

3 x^{5} - 20 x^{3}

f (x, y) = x^{2} + 3 y^{2} + 4 x - 9 y + 3

y = \frac{x}{x ^{2} - 1}

4 x^{4} + 4 y^{4} - x y

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