Applications of Limits and Derivatives

Abstract

The Intermediate Value Theorem (IVT) is the first application considered that uses concepts from the last three chapters. It is often considered an “obvious” result that has some important uses. The hypotheses in the IVT are very important and must be properly stated. The idea of the IVT is that a continuous function f(x) on an interval [a, b] cannot skip any values between f(a) and f(b), intermediate values. We consider one application of the IVT, the bisection method for finding zeroes of a function.