Question

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

Answer 1

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(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.