What is the difference between an extreme point and an extreme value of a function?
The difference between the extreme point and the extreme value of a function is more to do with notation.
If a function f(x) is plotted on a graph with the independent value on the x-axis and the dependent value f(x) on the y-axis, the extreme value is the y coordinate of the point at which the function has an extreme value. The extreme point would be the point with the coordinates (x, y). Extreme values of a function can be both minimum values as well as maximum values and include both local extreme value as well as absolute extreme values.
The extreme value is defined as a single number which is the value of f(x), an extreme point is defined as a pair of x and y coordinates.