Question

Can the absolute maximum and relative maximum be on the same point on a graph?

Answer 1

To me, the answer is NO.
Big, Bigger, Biggest
if you don't have Big and Bigger, the Biggest is a normal one, not a Big anymore.

Answer 2

A relative (or local) maximum is the highest point in a region. It may or may not be the absolute maximum of the function. The function f(x)=-x^2 has a local and absolute maximum at (0, 0).