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

Nov 13, 2015

$f$ has no critical numbers.

#### Explanation:

$f ' \left(x\right) = - \frac{4 \left({x}^{2} + 1\right)}{{x}^{2} - 1} ^ 2$

$f ' \left(x\right) = 0$ never

$f ' \left(x\right)$ does not exist only at $x = \pm 1$ neither of which are in the domain of $f$.

Therefore, $f$ has no critical numbers.