Highlights for High School Home > AP Calculus > Applications of Derivatives > Derivative as a Rate of Change

Derivative as a Rate of Change

Lecture Notes

Velocity (18.01 Fall, 2005)

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Section 1, Page 1

Average and instantaneous velocity formally defined as an introduction to the concept of a derivative. Includes a worked example.

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: None
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Practice Problem

Vertical Motion

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Problem 2 (page 2)

Finding the height and instantaneous velocity of a mass at a certain time after being dropped.

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: None

Solution (PDF) Pages 10 to 11

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Exam Questions

Automobile Crash Test

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Problem 5 (page 6)

Finding the position function and velocity of a car in an automobile crash test.

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: None

Solution (PDF) Pages 6 to 8

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Velocity and Rates of Change

Document PDF - 2.2 MB
Problem 1B-1 (page 2) to problem 1B-2 (page 2)

Two multi-part questions about a test tube falling off a building and a tennis ball bouncing upwards.

Course: 18.01 Single Variable Calculus, Fall 2006
Instructor: Prof. David Jerison
Prior Knowledge: None

Solution (PDF - 4.0 MB) Pages 3 to 4

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