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:
In this activity, we will start to become familiar with these words and their relationship to the first and second derivative. The second derivative is the derivative of the derivative. We will gain familiarity by studying the graphs of functions.
A list of definitions and theorems concerning vocabulary relating to the first derivative is available here, and a similar list for the second derivative is available here. The definitions are in the white boxes. Some are followed by examples that may require special browser plug-ins (so you can skip them if you are not sure how to make them work).
After you read the definitions, visit this page at the Visual Calculus web site. Work through all 10 exercises listed on the page. Some of the questions relate to the second derivative, if you have not yet learned about the second derivative (denoted by f''(x)), read section 3.8 in your book or revisit this page and read the definitions and consider the examples.
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, and answering the question "Did you find this activity useful?". [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 207, Vocab Activity'.