What are the critical values, if any, of $f (x) = \frac{4 x}{x^{2} - 1}$ $f(x)=(4x)/(x^2 -1)$ ?

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Answer 1 · 2015-11-13T17:16:47

$f$ $f$ has no critical numbers.

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

$f'(x) = 0$ 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.

What are the critical values, if any, of f(x)=(4x)/(x^2 -1)f(x)=4xx2−1f(x)=(4x)/(x^2 -1)?