Applications of Derivatives
In the previous chapter we focused almost exclusively on
the computation of derivatives. In this chapter will focus on applications of
derivatives. It is important to always remember that we didn�t spend a whole
chapter talking about computing derivatives just to be talking about them.
There are many very important applications to derivatives.
The two main applications that we�ll be looking at in this
chapter are using derivatives to determine information about graphs of functions
and optimization problems. These will not be the only applications however. We
will be revisiting limits and taking a look at an application of derivatives
that will allow us to compute limits that we haven�t been able to compute
previously. We will also see how derivatives can be used to estimate solutions
to equations.
Here is a listing of the topics in this section.
Rates of Change
- The
point of this section is to remind us of the application/interpretation of
derivatives that we were dealing with in the previous chapter. Namely, rates of
change.
Critical Points
- In
this section we will define critical points. Critical points will show up in
many of the sections in this chapter so it will be important to understand them.
Minimum and Maximum Values
- In
this section we will take a look at some of the basic definitions and facts
involving minimum and maximum values of functions.
Finding Absolute Extrema
- Here
is the first application of derivatives that we�ll look at in this chapter. We
will be determining the largest and smallest value of a function on an interval.
The Shape of a Graph, Part I
- We
will start looking at the information that the first derivatives can tell us
about the graph of a function. We will be looking at increasing/decreasing
functions as well as the First Derivative Test.
The Shape of a Graph, Part II
- In
this section we will look at the information about the graph of a function that
the second derivatives can tell us. We will look at inflection points,
concavity, and the Second Derivative Test.
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