# When using the first derivative test to find the critical points of a function, do you always have to include x=0?

Feb 11, 2017

Yes, if $0$ is in the function's domain. Note that if the derivative isn't defined at $0$, that is also a critical point.

#### Explanation:

That is because $0$ can be a critical point of a function. For example, consider the function $f \left(x\right) = {x}^{2}$.

$f ' \left(x\right) = 2 x$, and the root to the equation $f ' \left(x\right) = 0 \implies 2 x = 0$ is

$x = 0$.

At $0$, our $f$ also happens to have an absolute minimum, which wouldn't always be the case.

In fact, many such situations exist, so, unless $0$ is not in the functions domain, there is no reason why you wouldn't check what happens there.