Question

Can relative maximums and minimums be at the endpoints? I know global max/min can be at endpoints but I'm not sure about relative max/min.

Answer 1

No

Explanation:

Just because the derivative is 0 at a point doesn't necessarily mean it is a relative minimum or maximum. You must be able to evaluate the derivative on both sides of the point to determine if it changes signs. Since endpoints have only one side, they cannot be relative maximums or minimums.