lecture08 - 1 Related Rates So far we've been looking at...

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1 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. Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm 3 /s. How fast is the radius of the balloon increasing when the radius is 25 cm?
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