MA101: Single-Variable Calculus I

6.2: Related Rates

• You now know how to take the derivative with respect to the independent variable. In other words, you know how to determine a function's rate of change when given the input's rate of change. But what if the independent variable was itself a function? What if, for example, the input was a function of time? How do we identify how the function changes as time changes? This subunit will explore the answers to these questions.
  

• Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.2: Related Rates" URL

  Read Section 6.2 (pages 127-132). Another application of the chain rule, related rates problems apply to situations where multiple dependent variables are changing with respect to the same independent variable. Make note of the summary in the middle of page 128.
  

• Massachusetts Institute of Technology: David Jerison's "Newton's Method" Page

  Watch this video until 40:30. The majority of the lecture is about related rates, despite its title.
  

• Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Exercises 6.2: Problems 1, 3, 5, 11, 14, 16, 19, 20, 21, 25" URL

  Work through problems 1, 3, 5, 11, 14, 16, 19-21, and 25 for Exercise 6.2. When you are done, check your answers against Appendix A.