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


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.


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


Terms you should be able to define: hypothesis, conclusion, imply (i.e. mathematical implication), theorem, proof, existence theorem

Mini-Lectures and Examples

STUDY: Analysis of Curves - Extrema, CPs, MVT

Supplementary Resources (optional)

Video: The MVT and Related Results, Selwyn Hollis's Video Calculus

Lesson: The MVT and its Consequences, Dale Hoffman's Contemporary Calculus

rev. 2020-10-31