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Session 31: Related Rates

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Overview

The derivative tells us how a change in one variable affects another variable. Related rates problems ask how two different derivatives are related. For example, if we know how fast water is being pumped into a tank we can calculate how fast the water level in the tank is rising. The chain rule is the key to solving such problems.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Introduction to Related Rates (5 min)
» Accompanying Notes (PDF)

From Lecture 12 of 18.01 Single Variable Calculus, Fall 2006


» Clip 2: Related Rates (6 min)
» Accompanying Notes (PDF)

From Lecture 13 of 18.01 Single Variable Calculus, Fall 2006


» Clip 3: Rates: A Conical Tank (13 min)
» Accompanying Notes (PDF)

From Lecture 13 of 18.01 Single Variable Calculus, Fall 2006

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Recitation Video

 

Inflating a Balloon

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» iTunes U (MP4 - 17MB)
» Internet Archive (MP4 - 17MB)

Sliding Ladder

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» iTunes U (MP4 - 38MB)
» Internet Archive (MP4 - 38MB)

Worked Example

 

Solving an Optimization Problem Using Implicit Differentiation

 

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