Calculus on Demand at Dartmouth College Lecture 5 | Index | Lecture 7 Lecture 6

## Resources

Math 3 Course Syllabus
Practice Exams

# Contents

In this lecture we begin the actual study of calculus. We take a first look at modeling rates of change, and give an overview of the material of lectures 6-16 on the differential calculus.

### Quick Question

What is the slope of this line?

### Outline

Outline for Modeling Rates of Change

### Textbook

Modeling Rates of Change

### Quiz

Modeling Rates of Change Quiz

### Examples

• While skiing, Josh rides a chair lift moving at 3 miles per hour up a hill. After he has skied down the hill, his average velocity for the round trip is 5 miles per hour. How fast did he ski?
• Fill in the missing numbers in a derived table.
• A automobile testing organization runs cars around a speed track to test performance. One test involves running a car around a 1200-meter track at high speed, and recording the individual lap times and the average speed for the entire test. On one occasion, the results are recorded, but are missing the final lap time. The first 4 laps show times of 37 seconds, 25 seconds, 29 seconds, 27 seconds, and the average speed for the test is recorded as 112 miles per hour. Show that even without knowing the final lap time, we can conclude an error has most likely been made in recording the results.

### Applets

• Average Velocity
• Rate of Change
• Derived Function

### Videos

• Traveling 60 miles in half an hour gets you a speeding ticket
• Derived tables for x2

Lecture 5 | Index | Lecture 7