In the last chapter, we were introduced to derivatives in some detail, and thought about them as equations describing the instantaneous slope at any point of a curve. Then, we saw a few special cases. In this chapter, we will build on that background to do a few things. First, we explore what a derivative tells you about the curve it describes. We also look at how to think about “higher derivatives” — how the rate of change of a curve is itself changing. We can use this information to tell if a curve is coming to a maximum or minimum point, or perhaps changing direction. As a practical matter, we can use derivatives as a clue to how to draw a curve reasonably accurately.

The latter part of the chapter focuses ...

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