2019 CED – Unit 3: Differentiation: Composite , Implicit, and Inverse Functions

Unit 3 covers the Chain Rule, differentiation techniques that follow from it, and higher order derivatives. (CED – 2019 p. 67 – 77). These topics account for about 9 – 13% of questions on the AB exam and 4 – 7% of the BC questions. Topics 3.1 – 3.6 Topic 3.1 The Chain Rule. Students learn…

Did He, or Didn’t He?

Since it’s soon time to start derivatives, today we look at one way people found maximums and minimums before calculus was invented. Pierre de Fermat (1607 – 1655) was a French lawyer. His hobby, so to speak, was mathematics. He is considered one of the people who built the foundations of calculus. Along with Descartes,…

Limit of Composite Functions

Recently, a number of questions about the limit of composite functions have been discussed on the AP Calculus Community bulletin board and also on the AP Calc TEACHERS – AB/BC Facebook page. The theorem that we would like to apply in these cases is this: If f is continuous at b and , then .…

Infinite Musings

Students get confused about infinity, , because they think of it as a number, because used like a number. Even though they know there is no largest number, they think of infinity as the largest number. In studying limits, the starting point of calculus, infinite limits come up early on. We tell them . But…