Hello, member of the AP calculus list. What follows are some pages that I've mentioned on the list.

Find the Error: This is a list of fun calculus problems, all on the theme of finding an error in a bogus calculus proof that 2 = 1. They can help students to understand the details of concepts, emphasize the need for care when using calculus, and fill up the time between the AP exam and the end of the semester.

Car Talk: An automotive problem was asked on NPR's Cartalk, and the hosts were not able to solve it when they recognized that it was a Calculus problem. Three cheers to them for noticing! This link will take you to the problem, and my solution.

Todd's Evil Limit. My colleague, Todd Eisworth, walked into my office and showed this to me:

A noninflection point: During the grading of one of the AP exams, the question came up: Is it true that if f ' (x) < 0 for x < a, f ' (x) = 0 for x = a, and f ' (x) < 0 for x > a, does there have to be an inflection point of f at x = a? An equivalent question: If f ' (x) has a local maximum at x = a, does f ( x ) have to have an inflection point? The answer is "no", as shown by this counter-example, shown to me by Dave Bressoud.

A recursive function: I think this is just a fun thing to show your students.

The Lost Numbers Revealed: A mathematical interpretation of the numbers from the television show "Lost".

AP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this web-page. Doug is just this guy, you know?

Click here to go to Doug's homepage