Chapter 11
Differentiation and the Shape of Curves
IN THIS CHAPTER
Weathering the ups and downs of moody functions
Locating extrema
Using the first and second derivative tests
Interpreting concavity and points of inflection
Comparing the graphs of functions and derivatives
Muzzling the Mean Value Theorem — GRRRRR
If you’ve read Chapters 9 and 10, you’re probably an expert at finding derivatives. This is a good thing, because in this chapter you use derivatives to understand the shape of functions — where they rise and where they fall, where they max out and bottom out, how they curve, and so on. Then in Chapter 12, you use your knowledge about the shape of functions to solve real-world problems.
Taking a Calculus Road Trip
Consider the graph of 
in Figure 11-1.
Imagine that you’re ...
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