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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.
http://www.univie.ac.at/future.media/moe/galerie/diff1/diff1.html
- 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.
- 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.
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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.) |