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
windowmaximize 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

http://www.math.montana.edu/frankw/ccp/calculus/deriv/compare/learn1.mov
Play the following minimovie from the University of
Montana and notice the correspondences between increasing/decreasing
intervals and positive/negative intervals, as well as max/min
locations and xintercepts. Seeing the derivative being drawn
while the tangent line to the function is displayed demonstrates
what you have to do in the next task.

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.

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.

http://www.usna.edu/MathDept/website/courses/calc_labs/deriv/Deriv.html
Practice graphing the derivative on several different functions
provided by the javaapplet. Remember that your estimates are
roughly interpreted and you are trying to approximate xintercepts
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
 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
5question 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
888 level setting (versus the 465 setting shown below in the
screenshot image).
ii. a 10/10 mastery on a
difficulty 9 selection involving graphical transformations of the
derivative.
