# Mean Value Theorem & Geometric Consequences

This section contains documents created from scanned original files and other
documents that could not be made accessible to screen reader software. A "#"
symbol is used to denote such documents.

## Lecture Notes

#### The Mean Value Theorem

PDF
Section 5, Page 4 to page 5

The Mean Value Theorem is briefly defined.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Application of the Mean Value Theorem

PDF
Section 1, Page 1

Mean Value Theorem used to solve error analysis problem involving the precision of a device's signal output.

Instructor: Prof. Jason Starr
Prior Knowledge: Mean Value Theorem (section 5 of lecture 8)

#### The Mean Value Theorem Revisited

PDF
Section 2, Page 1 to page 2

Review of Mean Value Theorem, with introduction of Generalized Mean Value Theorem.

Instructor: Prof. Jason Starr
Prior Knowledge: Mean Value Theorem (section 5 of lecture 8)

#### Mean Value Theorem

PDF#

Definition and explanation, including Rolle's Theorem.

Instructor: Prof. David Jerison
Prior Knowledge: None

## Online Textbook Chapter

#### Accuracy of Approximations, and the Mean Value Theorem

Document

Finding the error in an approximation of a function, leading to the Mean Value Theorem.

Instructor: Prof. Daniel J. Kleitman

## Exam Questions

#### Mean Value Theorem

PDF - 2.2 MB#
Problem 2G-1 (page 18) to problem 2G-8 (page 19)

Eight questions which involve showing or proving statements using the Mean Value Theorem, including a question about speeding on the Massachusetts Turnpike.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Mean Value Theorem

PDF
Problem 8 (page 1)

Stating the theorem and using it to prove two statements about functions.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Mean Value Theorem

PDF
Problem 6 (page 1)

Using the theorem to justify two statements.

Instructor: Prof. David Jerison
Prior Knowledge: None