What are the critical points of $(\frac{x^{2}}{x^{2} - 1})$ $(x^2/(x^2-1))$ ?

Question

What are the critical points of $(\frac{x^{2}}{x^{2} - 1})$ $(x^2/(x^2-1))$ ?

1 Answer

Impact of this question

10075 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-28T22:48:20

I will put f(x) in front of $(\frac{x^{2}}{x^{2} - 1})$ $(x^2/(x^2-1))$

To find the critical number, you must get the first derivative of
f(x) = $(\frac{x^{2}}{x^{2} - 1})$ $(x^2/(x^2-1))$

The first derivative is $f^'(x) = (-2x)/(x^2-1)^2$

Now you must set $f^'(x) = 0$ , and you must also find where the $f^'(x)$ does not exist (dne).

$f^'(x) = 0$ ------------------------- $f^'(x)$ dne

$(-2x)/(x^2-1)^2$ = 0 ------------------ $f^'(x)$ dne at x = 1 and x = -1

-2x = 0
x = 0 ------------------------------now you must plug them back to the
---------------------------------------- back to the original equation.
---------------------------------------Since x = 1 and x = -1 are undefined, they --------------------------------------------------------are not critical numbers

Since x = 0 is defined in the original equation, it is a critical number.

Science

Math

Humanities

... and beyond

What are the critical points of $(\frac{x^{2}}{x^{2} - 1})$ $(x^2/(x^2-1))$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What are the critical points of (x^2/(x^2-1))(x2x2−1)(x^2/(x^2-1))?

1 Answer

Related questions

Impact of this question

What are the critical points of $(\frac{x^{2}}{x^{2} - 1})$ $(x^2/(x^2-1))$ ?