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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Thursday, October 13, 2005

### Online Class #1: Critical Numbers

Tomorrow's class will be done entirely online in the iMac Lab, Room 58. Here we go ....

We will be learning how to use derivatives to find local minima (the plural form of minimum) and maxima (the plural form of maximum) for a given function. We'll be looking at lots of graphs to see if we can identify the relationship between:

i)  The roots of a derivative function, and
ii) where (the x-coordinate) its parent function has a maximum or minimum.

1. Watch this tutorial where we look at a cubic function.

2. Read through this tutorial. All the graphs are interactive. See what happens when you move the mouse over the graphs or pictures. Don't calculate any derivatives algebraically; use your calculators to create the graphs of derivative functions using the nDeriv command ([Math]:[8]). We'll learn the algebra next week. ;-) Pay attention to how the derivative changes where the parent function has a local max or min.

3. Look up the definition of a Critical Number (follow the link to the definition of a stationary point as well). Write it down, in your own words in your notebook.

4. Your assignment is in your textbook. You can review the introduction to this topic on pages 114 and 115. Then do all the ODD numbered exercises beginning on page 116. Also do questions #10, 16 and 22.

If you have the time, comment on this post and let me know what you thought of this lesson. Did you enjoy having the entire lesson online? What were the advantages and disadvantages of learning this way? Should we do this again? Why or why not?

Have a great day and do someone a good turn for no good reason. ;-)

Cheers,
Mr. K.