What are the critical numbers for $f(x)= x/(x+1)$ ?

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Answer 1 · 2015-06-13T12:34:41

This function has no critical numbers.

A critical number for $f$ is a number in the domain of $f$ at which the derivative is either $0$ or fails to exist.

For $f(x) = x/(x+1)$ , the derivative is:

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

$f'(x)$ is never $0$ and

$f'(x)$ is undefined at $x=-1$ , but $-1$ is not in the domain of $f$ ,

So, $f$ has no critical numbers.

What are the critical numbers for f(x)= x/(x+1)f(x)= x/(x+1)?