Differentiation—Applications
Derivatives are used to describe dynamic situations, i.e. situations where change in one quantity produces a change in another. Indeed, the difference quotient (see Definition 8.1.1) measures the ratio of the change in f(x) to the change in x, and its limit is the derivative f ′(x). In this chapter, we develop theories which allow us to investigate such situations.
In many applications, it is important not merely to solve a problem, but to find the solution which is, in some sense, optimal. For example, there are infinitely many rectangles having a given perimeter, but the square is the choice which gives the maximum area. We will see that differentiation can be used to locate optimal (i.e. extremal) values. ...
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