Ms. Meyer’s Weblog

Web Assignment 3 January 2, 2008

Click on 3. Calculus Applets or go to http://www.ies.co.jp/math/java/calc/index.html and click on “Average Rate of Change and Derivatives.” Read the example and then answer the question by using the tool. Play with it for a bit so you know how it works. Then answer the following questions:

1. When we make h smaller, what does (f(a+h)-f(a))/h approach when y=x^1/2? Is this answer different than the one asked in the example? Why or why not?
2. Does it matter if (f(a+h)-f(a))/h is negative? What does (f(a+h)-f(a))/h approach then? Explain.
3. Pick one function and make a graph of the values of h and a. ( h=y and a=x type graph) Plot the points on the graph and then explain what happened to both when the values were large verses small.

After you finish that hit the back button, 3. Calculus Applets or go to http://www.ies.co.jp/math/java/calc/index.html again. Then click on “Surfing (Derivatives.)” While moving the red dot under the surfer’s feet watch the green bar and what happens to it. Do you notice any similarities to the previous graph?

Next, click on the Trace Box and then move the red dot along the line again. Watch what happens under the surfer. Note: You may have to trace the line a couple times to see what happens under the surfer clearly.
1. Tell me what you think is happening.
2. What do you think it means?
3. Is there a correlation between this and the previous problem?

This is an individual assignment. However, we will discuss it later in our groups and as a class, so don’t panic. After you have completed this, please turn it in at the end of class. If you finish early feel free to check out the other fun examples on that page or to get a head start on the homework for tonight.