Critical Numbers of a Rational Function

There are infinitely many critical numbers because the derivative is a constant positive value, indicating no change in the behavior of $f(x)$.

The function has no critical numbers because its derivative $f'(x)=\frac{1}{(x+1)^2}$ is always positive for $x\neq -1$, and $x=-1$ is not in the domain.

Critical numbers occur where the derivative is undefined; hence, $x=-1$ is the unique critical number of $f(x)$.

The only critical number is $x=-1$, where the derivative is zero.