The last calculus project is a sample interactive enhancement of a problem from a high school calculus text: Calculus and Advanced Functions (McGraw-Hill Ryerson Canada). The problem occurs on page 395 of the text and concerns minimizing the time required to complete a bike race. The exploration in the book expects the student to use TI-Interactive to solve the problem, first using derivatives and then using a spreadsheet.

I built a simulator for the problem, first in Geometer’s Sketchpad and then in Flash 6, and extended the original two-part problem to a ten-part activity. The complete exploration has three consecutive phases: exploration using the simulation, deriving the answer by calculation and deriving a formula for answer.

(The simulation occasionally breaks after the page containing it is reloaded – I’m not sure why. It was built when I was just beginning to learn Actionscript, so there’s likely some obscure error in its code that I haven’t found.)