AP Calculus:  Curve Sketching with First and Second Derivatives 
Web Exploration II

This curve sketching web activity consists of three main tasks and makes use of java applets from the Maths Online website below.  All links will open in a new window.


  1. On the Definition of the Derivative
    Slide the arrows left and right to explore the relationship between the function and its derivative.  Answer the questions about the zeros of both the function and its derivative, as asked on the accompanying worksheet.
  2. Derivative Puzzles 1, 2, and 3
    For each of these applets, arrange the graphs in vertical columns so that the derivative appears below each function;  that is, the top row represents the functions, the middle row represents the first derivatives, and the bottom row represents the second derivatives.  Once you have placed all the graphs correctly (be sure to check your solutions!) sketch them on your worksheet.
  3. Big Derivative Puzzle
    Match each of the four functions with its derivative (a perfect score is 10) and sketch your results on the provided axes.  In the space below the axes, map your critical thinking processes as you identify key information. Load a new set of functions and repeat the mapping process a second time.

Click Here for the Accompanying Worksheet
(It is printable and about 3 pages long.)