Note as well that in order for a point to be a relative extrema we must be able to look at function values on both sides of x=c to see if it really is a maximum or minimum at that point. This means that relative extrema do not occur at the end points of a domain. They can only occur interior to the domain.

Is an endpoint a relative extrema?

Relative extrema can certainly occur at endpoints of a domain. For instance, the function f(x) = x on the interval [0, 1] has a relative maximum at x = 1 and a relative minimum at x = 0.

Can an endpoint be an extrema?

Critical Values That Are Not Extrema

A function's extreme points must occur at critical points or endpoints, however not every critical point or endpoint is an extreme point.