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MA101: Single-Variable Calculus I

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  6. Unit 6: Applications of the Derivative
  7. 6.2: Related Rates
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  • 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.

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MA101: Single-Variable Calculus I
Sections
Course Introduction
Unit 1: Analytic Geometry
Unit 2: Instantaneous Rate of Change: The Derivative
Unit 3: Rules for Finding Derivatives
Unit 4: Transcendental Functions
Unit 5: Curve Sketching
Unit 6: Applications of the Derivative
Unit 7: Integration
Unit 8: Applications of Integration
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