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