Objectives: In this tutorial, we investigate two important properties of functions which are continuous on a closed interval [a, b]: the Intermediate Value Theorem and the Extreme Value Theorem. As an application of the Intermediate Value Theorem, we discuss the existence of roots of continuous functions and the bisection method for finding roots.

After working through these materials, the student should be able to apply the Intermediate Value Theorem, to determine whether certain functions have roots, and use the bisection method to find roots to any degree of accuracy.