Question

Is there any distinction between an extreme point and an extreme value of a function?

Answer 1

A point has two or more dimensions. In 2-space (3,10), while the extreme value is 10.

For example take the downward pointed parabola, (y - 3) = (x + 4)^2. It's extreme value is y = 3. It's extreme point is the vertex (3, -4)

The same concept carries on to higher dimensions.