In chapter 4 of the book, and in the last web activity, we have been learning about the first and second derivatives of a function and what they can tell us about the structure of the graph of function (helping us to better understand the function).  We will now begin combining all of this information to further our understanding and, as a result, we will be able to construct the key features present in the graph of the function.  At this web-site, titled Graphing using first and second derivatives, there are 11 completely worked out examples (you can ignore #9) showing how to combine the information from the first and second derivatives with a few extra details about the function (for example intercepts and asymptotes) to produce a detailed graph of the function.  Work through these examples and be sure you can produce all of the first and second derivative sign distributions.  Try to understand how the information from the sign distributions fits together to help produce the graph of the function. 

Read the problems and solutions at the web site listed above and then apply the graphing process to the following function:

1. Which of the examples (listed in the above web site) is this problem most similar to?
2. What are the critical values (if any)?
3. Which critical values are at local minimums?
4. What are the inflection points (if any)?
5. Is there a horizontal asymptote? If so, what is it?

If your email program is configured properly, you can click on the name of your instructor (below) to send the email. Use the subject line `Your Name, Math 175, Graphing a Function Activity'.

• Dr. Peirce (peirce.jame@uwlax.edu)