When calculating the extremas, is there really a difference between relative and absolute extremas? Or are they just used interchangeably?

Answer 1

absolute means global. It's possible to have several relative extrema, and some, all, or none may be absolute extrema.

A parabola has one relative extremum, which is absolute.

A cubic such as y=(x-1)(x-2)(x-3) has two relative extrema, but no absolutes at all, since the function goes off to infinity in both directions.

a quartic like y=(x-1)^2 * (x-2)^2 has 3 relative extrema; one max and 2 min, but only the minima are global since y goes off to +infinity, but never gets less than zero.

Start tossing in exponentials and logs, and trig functions, and things can get complicated.