There are many attributes of a function that the derivative can help us analyze. These various attributes have names and descriptions, many of which containing words from the following list:

• increasing
• decreasing
• critical point
• relative (or local) maximum or minimum (extrema)
• concave up
• concave down
• inflection point

In this activity, we will become familiar with these words and their relationship to the first and second derivative. We will gain this familiarity by studying the graphs of functions.

Start by visiting this page at the Visual Calculus website.  Work through all 10 exercises listed on the page.In each exercise you'll need to identify all of the points on the graph with the desired property. 

Send your instructor an email stating the answers to exercise 4. [Hint: the answer to question 5 is B and F, can you see why?] 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, Vocab Activity'.

• Dr. Peirce (peirce.jame@uwlax.edu)