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Related Rates
So far we’ve been looking at the rate of change of one “thing”. Maybe it’s a particle or just a function or
what have you. A lot of the time, however, when something changes it causes something else to change.
For instance, say you’re pumping air into a balloon. The volume, radius, and surface area of the balloon all
change. The thing is, we can relate all of these quantities so we can relate the rate of change.
This method lets us ﬁnd the rate of change of some quantity if we have the rate of change of something
else. Another example is two cars travelling in diﬀerent directions. Their individual rate of change relates
to the rate of change of the distance between the two cars.
There are two basic steps in this kind of problem:
1. Find an equation that relates the quantities in the problem.
2. Use implicit diﬀerentiation to get the rate of change that you want.
Example 1.1.
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This note was uploaded on 02/29/2008 for the course MAT 141 taught by Professor Varies during the Spring '08 term at Lehigh University .
 Spring '08
 varies
 Rate Of Change

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