# Lesson Plan: The Extreme Value Theorem and Rolle’s Theorem

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to interpret and use the extreme value theorem and Rolle’s theorem.

#### Objectives

Students will be able to

• understand the extreme value theorem and when its conditions are satisfied,
• understand Rolle’s theorem and when its conditions are satisfied,
• understand the different ways in which Rolle’s theorem can be satisfied,
• find points in an interval that satisfy Rolle’s theorem for a given function.

#### Prerequisites

Students should already be familiar with

• differentiation (including the chain, product, and quotient rules),
• the concept of continuity (not necessarily the formal definition),
• critical points of a function,
• classifying a critical point as a local minimum or maximum using the first derivative test,
• the distinction between local and absolute minima or maxima.

#### Exclusions

Students will not cover

• mathematical proof of the extreme value theorem,
• the mean value theorem.