Surprising Results Using Calculators for Derivatives.

How does the numerical derivative on the calculator compare with the actual derivative? hen is the numerical derivative obtained on the calculator greater than the actual derivative and when is it smaller?" A group of college professors and high school mathematics teachers attending a workshop seemed not to know the answer. The question was posed by Deborah Hughes-Hallett, then of Harvard University, who is currently at the University of Arizona, at the first Technology Intensive Calculus for Advanced Placement (TICAP) institute at Clemson University in spring 1992. She posed the question when investigating the curves = 3. The second derivative was a popular suggestion as a possible predictor, and the author's initial thoughts centered on the concavity of the curve as relating to the answer. This article attempts to answer Hughes-Hallett's question and to generalize the results. As technology changes what and how we teach, the symmetric difference emerges as an interesting topic for students' exploration. The numerical derivative function on most graphing calculators approximates the derivative by averaging the for ward and backward difference quotients