Questions to think about and discuss with your neighbor: 1) What is the horizontal distance between P and A? (not a number, an expression) 2) What is the vertical distance between P and A? (If you need a hint, click the check box) 3) What is the equation for the slope of the red (secant) line? Does this seem like anything we've heard of? 4) What happens as we let h get larger or smaller? (Use the slider at the top) 5) Click on the Tangent Line checkbox. What would be an expression for the slope of the Tangent Line? 6) So what's the whole point here?

Your task here is to study extrema (maximums and minimums.) Look at each of the 6 examples individually (make sure you only have one checked at a time.) On each you are given a point that you can drag and look at coordinates. Answer the questions below.

1) In each example, find the maximums and minimums. 2) There are two classifications of maximums and minimums. See if you can determine the different types. Check the hint if necessary. 3) There is something called the extreme value theorem, which states that under certain conditions, a function will always have a maximum and a minimum. See if you can determine what these conditions are (There are two of them.) Examine the functions that had maximums and minimums and those that didn't.)