Chapter 4 Day 2. What if the graph has an asymptote or two?? Find the first derivative. Put zeroes on a number line Find the second derivative. Put zeroes.

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Presentation transcript:

Chapter 4 Day 2

What if the graph has an asymptote or two?? Find the first derivative. Put zeroes on a number line Find the second derivative. Put zeroes on a number line Lets look at the graph here:here:

What do we do? The same general process holds. 1.Find vertical asymptotes and create “areas” 2.Use f′(x) and determine max/min points in each area. Plot these points 3.Use f′′(x) to determine concavity in each area. Plot these points. 4.If horizontal asymptotes exist, use them to finish off the graph 5.Plot x, y intercepts.    Use numerator AND denominator zeroes! Things can change around an asymptote

Examples