Unit 4 covers rates of change in motion problems and other contexts, related rate problems, linear approximation and L’Hospital’s Rule. (CED – 2019 p. 82 – 90). These topics account for about 10 – 15% of questions on the AB exam and 6 – 9% of the BC questions.
Topics 4.1 – 4.6
Topic 4.1 Interpreting the Meaning of the Derivative in Context Students learn the meaning of the derivative in situations involving rates of change.
Topic 4.2 Linear Motion The connections between position, velocity, speed, and acceleration. This topic may work better after the graphing problems in Unit 5, since many of the ideas are the same. See Motion Problems: Same Thing, Different Context
Topic 4.3 Rates of Change in Contexts Other Than Motion Other applications
Topic 4.4 Introduction to Related Rates Using the Chain Rule
Topic 4.5 Solving Related Rate Problems
Topic 4.6 Approximating Values of a Function Using Local Linearity and Linearization The tangent line approximation
Topic 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms. Indeterminate Forms of the type and . (Other forms may be included, but only these two are tested on the AP exams.)
Topic 4.1 and 4.3 are included in the other topics, topic 4.2 may take a few days, Topics 4.4 – 4.5 are challenging for many students and may take 4 – 5 classes, 4.6 and 4.7 two classes each. The suggested time is 10 -11 classes for AB and 6 -7 for BC. of 40 – 50-minute class periods, this includes time for testing etc.
Posts on these topics include:
Good Question 9 – Related rates
Here are links to the full list of posts discussing the ten units in the 2019 Course and Exam Description.
2019 CED – Unit 4 Contextual Applications of the Derivative Consider teaching Unit 5 before Unit 4
2019 – CED Unit 5 Analytical Applications of Differentiation Consider teaching Unit 5 before Unit 4
2019 – CED Unit 7 Differential Equations Consider teaching after Unit 8
2019 – CED Unit 8 Applications of Integration Consider teaching after Unit 6, before Unit 7