Rates of Change
The purpose of this section is to remind us of one of the
more important applications of derivatives. That is the fact that
 represents
the rate of change of
 .
This is an application that we repeatedly saw in the previous chapter. Almost
every section in the previous chapter contained at least one problem dealing
with this application of derivatives. While this application will arise
occasionally in this chapter we are going to focus more on other applications in
this chapter.
So, to make sure that we don�t forget about this
application here is a brief set of examples concentrating on the rate of change
application of derivatives. Note that the point of these examples is to remind
you of material covered in the previous chapter and not to teach you how to do
these kinds of problems. If you don�t recall how to do these kinds of examples
you�ll need to go back and review the previous chapter.
Example
Determine all the points where the following function is not changing.
Solution
First we�ll need to take the derivative of the function.
Now, the function will not be changing if the rate of
change is zero and so to answer this question we need to determine where the
derivative is zero. So, let�s set this equal to zero and solve.
The solution to this is then,
If you don�t recall how to solve trig equations check out
the >
Solving Trig Equations sections in the Review Chapter.
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