Question

What are the critical values, if any, of `f(x)=(4x)/(x^2 -1)`?

Answer 1

`f` has no critical numbers.

Explanation:

`f'(x) = -(4(x^2+1))/(x^2-1)^2`

`f'(x) = 0` never

`f'(x)` does not exist only at `x=+-1` neither of which are in the domain of `f`.

Therefore, `f` has no critical numbers.