2.1 Modeling Rates of Change
By the end of your studying, you should know:
On-screen applet instructions: This applet shows the average rate of change at x = a, where a can be chosen from the pull down list. A single click in the graph gives an enlarged picture around the point x = a. Another click restores the original size. The value of h can be set on the slider. Click here for further instructions.
ExamplesWhile 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?
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.
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 2.1 Modeling Rates of Change (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
|1.7 Case Study: Modeling with Elementary Functions||Table of Contents||2.2 The Legacy of Galileo, Newton, and Leibniz|
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel