Are there any rules concerning when to use the word 'extreme' and when to use 'extremal'? For instance, in a convex set you speak of an 'extreme point', while there is also usage of 'convex extremal functions'.
In my opinion one use the word 'extremal' in the sense of calculus of variation. So if you have to minimize/maximize a functional over some functions or curves. But if you maximize or minimize over a set of points you speak about 'extreme'.