Linear Motion (Type 2)

AP Questions Type 2: Linear Motion We continue the discussion of the various type questions on the AP Calculus Exams with linear motion questions. “A particle (or car, person, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation (most often), or the acceleration equation of something…

Extreme Average

A recent post on the AP Calculus bulletin board observed that the maximum value of the average value of a function on an interval occurred at the point where the graph of the average value and the function intersect. I am not sure if this concept is important in and of itself, but it does…

Open or Closed?

About this time of year, you find someone, hopefully one of your students, asking, “If I’m finding where a function is increasing, is the interval open or closed?” Do you have an answer? This is a good time to teach some things about definitions and theorems. The place to start is to ask what it…

Reading the Derivative’s Graph

A very typical calculus problem is given the equation of a function, to find information about it (extreme values, concavity, increasing, decreasing, etc., etc.). This is usually done by computing and analyzing the first derivative and the second derivative. All the textbooks show how to do this with copious examples and exercises. I have nothing…