Recognizes the absolute extrema & relative extrema for the given function.

 f ( x ) = x²       on                  [-2, 2]

Solution

Following is the graph for this function.

In this case still we contain a relative & absolute minimum of zero at x = 0 .  Still we also have an absolute maximum of four. This will occur at two points, x = -2 and x = 2 .

Again, the function doesn't contain any relative maximums.

As this instance has illustrated there can only be a single absolute maximum or absolute minimum value, but they can occur at more than one place in the domain.