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Course: Calculus I
Topic: Analysis of Curves
Subtopic: Mean Value Theorem for Derivatives

Overview

This lesson covers two theorems, the Mean Value Theorem for Derivatives (MVT) and Rolle's Theorem. Rolle's Theorem is a special case of the MVT. Both theorems require continuous differentiable functions and show that there is a point at which the tangent line has a specific given slope. These theorems are primarily used to prove other (more practical) calculus theorems.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.2.1 Understand the hypothesis and conclusion of Rolle's Theorem
• 3.2.2. Apply Rolle's Theorem to show that there exists a c-value where the tangent line is horizontal
• 3.2.3 Understand the hypothesis and conclusion of the Mean Value Theorem for Derivatives
• 3.2.4. Apply the Mean Value Theorem to show that there exists a c-value where the tangent line is of the required slope
• 3.2.5 Understand Rolle's Theorem and the Mean Value Theorem from both an algebraic and graphical perspective

Terminology

Define: hypothesis, conclusion, imply (i.e. mathematical implication), theorem, proof, existence theorem

Supplementary Resources (optional)