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The Calculus Lifesaver by Adrian Banner

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CHAPTER 12 _____________________________

Sketching Graphs

Now it’s time to look at a general method for sketching the graph of y = f(x) for some given function f. When we sketch a graph, we’re not looking for perfection; we just want to illustrate the main features of the graph. Indeed, we’re going to use the calculus tools we’ve developed: limits to understand the asymptotes, the first derivative to understand maxima and minima, and the second derivative to investigate the concavity. Here’s what we’ll look at:

• the useful technique of making a table of signs;

• a general method for sketching graphs; and

• five examples of how to use the method.

12.1 How to Construct a Table of Signs

Suppose you want to sketch the graph of y = f(x). For any ...

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