AP Calculus:  Curve Sketching the First Derivative
Web Exploration I

This curve sketching web activity consists of five main tasks and makes use of applets and movies from the U.S. Naval Academy, the University of Montana, and the WWW Interactive Mathematics Server as indicated below.  All links will open in a new window--maximize it while working on each task, and close it to return to this page.

PART 1 - Interpreting and Sketching the Derivative of a Function 
                 USNA Derivative Applet

1. http://www.math.montana.edu/frankw/ccp/calculus/deriv/compare/learn1.mov
   Play the following mini-movie from the University of Montana and notice the correspondences between increasing/decreasing intervals and positive/negative intervals, as well as max/min locations and x-intercepts.  Seeing the derivative being drawn while the tangent line to the function is displayed demonstrates what you have to do in the next task.
    
2. http://www.usna.edu/MathDept/website/courses/calc_labs/deriv/Application.html
   Read the two examples about volume of a balloon and traffic patterns presented as an introduction to interpreting and  sketching the derivative of a function.
3. http://www.usna.edu/MathDept/website/courses/calc_labs/deriv/MathReview.html
   Read the examples about how to sketch the graph of a derivative and learn about the applet you will use in task 4.
   
4. http://www.usna.edu/MathDept/website/courses/calc_labs/deriv/Deriv.html
   Practice graphing the derivative on several different functions provided by the java-applet.  Remember that your estimates are roughly interpreted and you are trying to approximate x-intercepts and general shape of the derivative.  Check the amount of visual error as a measure of your accuracy.  You may want to sketch the general shape on paper at first, because you must draw with your mouse from left to right continuously.
   

PART 2 - Recognizing the Graph of the Derivative of a Function 
                 WIMS Mastery Quiz

4. http://wims.unice.fr/wims/wims.cgi?session=NXC576D488.2&+lang=en&+module=U1%2Fanalysis%2Fgraphder.en
   The WWW Interactive Mathematics Server (WIMS) provides the opportunity to measure mastery of recognizing the derivative of a function graphically.  You are to use the DETAILED MENU link navigate to the webpage below and set the parameters as I have shown in the image.  Your goal is a 10/10 score on a 5-question quiz generated with the parameters shown in the screenshot below...however, if that seems too easy, try the settings that follow for more challenging problems:
          i.  a 10/10 mastery on an 8-8-8 level setting (versus the 4-6-5 setting shown below in the screenshot image).
         ii.  a 10/10 mastery on a difficulty 9 selection involving graphical transformations of the derivative.