# Possible Points of Local Extrema

I know that we should check critical numbers (points where f'(x) is either zero or not defined) and endpoints (for a closed interval) as possible points of local extrema of f(x). Obviously, all these points should be in the domain of f. So why does the following problem also test x = 0, which is not in the domain of f?

• How come do you claim they test $0$? Nov 22, 2014 at 14:36

In order for the testing to work, the function must be continuous on the entire test interval. This function is not continuous (or even defined) at $x=0$. As you can see, the function in fact changes direction as one moves from the left to the right of 0.