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Lecture Notes
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Section 1, Page 1 to page 2
Related rates description. Example problem using Hooke's law.
Prof. Jason Starr
The Chain Rule and Implicit Differentiation (sections 4 and 5 of lecture 4)
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Section 2, Page 2 to page 4
Step-by-step guide to solving related rates problems. Worked examples involving a speeding driver and a point moving on the x-axis.
Prof. Jason Starr
Related Rates (section 1 of this lecture) and Implicit Differentiation (section 5 of lecture 4)
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PDF
Section 4, Page 5 to page 6
Related rates worked example.
Prof. Jason Starr
Related Rates (section 1 of lecture 11)
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Exam Questions
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Problem 1 (page 2)
Finding the rate at which a particle moving on the x-axis is moving away from a point on the y-axis.
Prof. Jason Starr
None
Solution (PDF) Page 1
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Problem 6 (page 1)
Finding the rate of change of a particle's distance from the y-axis as it moves around the unit circle.
Prof. Jason Starr
None
Solution (PDF) Pages 2 to 3
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Problem 3.3 (page 2) to problem 3.4 (page 2)
Two problems which involve a melting icicle and a melting block of ice.
Prof. Jason Starr
None
Solution (PDF) Pages 13 to 15
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Problem 8 (page 1)
Finding the rate of change of the radius of a balloon with decreasing volume.
Prof. David Jerison
None
Solution (PDF)# Page 6
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Problem 10 (page 1)
Finding the time for a substance to decay to one-fourth its original amount, and the rate at which it is decaying at this time.
Prof. David Jerison
None
Solution (PDF)# Page 7
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Problem 5 (page 1) to problem 6 (page 1)
Two questions involving the rate of change of the angle of a falling tree and the rate of change of the water level in a cone.
Prof. David Jerison
None
Solution (PDF)# Page 2
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Problem 4 (page 1)
Finding the rate at which a prisoner needs to run to stay ahead of a searchlight
Prof. David Jerison
None
Solution (PDF)# Page 1
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Problem 4 (page 1)
Finding the rate of change of the angle at which a person is watching a rocket ten seconds after it takes off
Prof. David Jerison
None
Solution (PDF)# Page 2
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Problem 5 (page 1)
Finding the rate at which the shadow of a falling Christmas tree is lengthening.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF - 2.2 MB
Problem 2E-1 (page 16) to problem 2E-10 (page 17)
Ten questions which include finding the rate of change of a robot's shadow, the rate at which the distance between two boats is increasing, and the rate of change of the thickness of oil in a frying pan.
Prof. David Jerison
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