Anton and some other idiots use the words
``relative'' and ``absolute'' to mean ``local'' and ``global''.
This is totally unnecessary training wheels
``relative'' is a confusing word too: relative to what?

Students learn ``local'' and ``global'' quickly -- they have geometric
meaning!

``extrema'' is a fancy word, and ``max/min'' is usually clearer.

``critical point'' and ``critical value'' are okay words, but
shouldn't be introduced in this context -- they're unnecessary.
``point/value'', otoh, is a good separation which should be
emphasized, and early!
...they should be contrasted with -regular-!

Further, ``critical'' should be understood in terms of dynamics and
mapping: at a critical point, the derivative isn't injective
(oops...), and maybe the function does something ugly locally,
in contrast to its nice behaviour at ``regular'' points.

You can also call 'em ``stationary points'';
formally, a critical point is where $df=0$ -or- is undefined,
while a stationary point is just where $df=0$:
it's where a partical moving -stops-.

However, most fancy math folk just work with smooth functions, so in
this context critical point -means- stationary
(and no-one says ``stationary'').
