MA005: Calculus I

The Intermediate Value Theorem is an example of an "existence theorem" because it concludes that something exists: a number $\mathrm{c}$ so that $\mathrm{f}(\mathrm{c})=\mathrm{V}$. Many existence theorems do not tell us how to find the number or object which exists and are of no use in actually finding those numbers or objects. However, the Intermediate Value is the basis for a method commonly used to approximate the roots of continuous functions, the Bisection Algorithm.