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

Jun 13, 2015

This function has no critical numbers.

#### Explanation:

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 $f \left(x\right) = \frac{x}{x + 1}$, the derivative is:

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

$f ' \left(x\right)$ is never $0$ and

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

So, $f$ has no critical numbers.