Do your sources say thecan'tbe relative extrema or that they might not be?

For example, a "relative extremum" (a relative minimum) of on the interval [0, 1] is at x= 0, an end point.

Strictly speaking, I would say that x= 1 is also a relative maximum because it is larger than any nearby value of the functionin that interval.

Of course, it is not a "critical point"- the derivative is not 0 at x= 1. x= 0 is both an endpoint of the interval and a critical point of the function.