Is it possible for relative (aka local) minima/maxima to be located at closed endpoints?

There is this problem that asks me to identify relative/local maxima on a derivative graph. So I located all the places that the graph cross the x-axis and then narrow my options to locations in which the graph crosses the x-axis and shoots downward negatively (1st derivative test).

But what about closed endpoints (NOT open endpoints because critical numbers don't exist there) that are located right on the x-axis and "would've" became negative? If not, then under what conditions can closed (not open) endpoints be defined as a extremum? I'm confused; I'd appreciate some clarification.

By the way, the book didn't include the endpoint as a relative maximum.