This applet is almost identical to the previous one about extrema on an open interval, except that now we're considering a closed interval. The two sliders again allow you to change the location of the endpoints [math]\left( a, f\left(a\right) \right)[/math] and [math]\left( b, f\left(b\right) \right)[/math].
As you change the locations of the endpoints, see if you can create intervals with the following:
[list]
[*]Absolute maximum, absolute minimum, relative maximum, and relative minimum which are all different.
[*]Absolute maximum equals relative maximum, absolute minimum and relative minimum are different.
[*]Absolute minimum equals relative minimum, absolute maximum and relative maximum are different.
[*]Absolute maximum equals relative maximum and global minimum equals relative minimum.
[*]Absolute maximum and absolute minimum exist, only a relative minimum exists.
[*]Absolute maximum and absolute minimum exist, only a relative maximum exists.
[*]Absolute maximum and absolute minimum exist, there are no relative extrema.
[/list]
