The Extreme Value Theorem

Objectives:
Students will be able to visualize the Extreme Value Theorem and better understand how to find absolute maximums and minimums.

After typing in a function, click on the drop-down menu to find the critical points that are in the interval. Type these x-values into the c1, c2, c3, c4 input boxes depending on the number of critical values present.

Questions:
1. Can the absolute maximum be one of the endpoints or does it have to be a critical point? What about the absolute minimum?
2. Can f(x) ever be a noncontinuous function? What if the left and right endpoints are not included? Will the Extreme Value Theorem hold?

Janel Warren, 18 November 2013, Created with GeoGebra