Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 3.2

1. Review question: What is the general form for a quadratic function?
2. What is the general form for the derivative of a quadratic function?
3. A function p(x) has a parabola as its graph, and it satisfies p(0) = 1 and p'(0) = 1. Can you determine the function? If not, give at least two possibilities.
4. Explain why it makes sense that velocity is the derivative of a height function, and acceleration is the derivative of the velocity function. Use the rate of change way of thinking about derivatives.
5. At the bottom of page 195, the book uses the term ``stationary points''. We skipped over this (we will get back to it though). Use the index of your book to find where the definition of ``stationary point'' is and write it here.
6. Go back to page 103 and check out the graphs of the height and velocity functions there (reread Example 4 on that page too). What is the velocity (the derivative) when the height is maximum? Explain in your own words why it makes sense that ``for a differentiable function f, local maxima and minima can occur only at stationary points.''
7. Why do you also have to check endpoints when searching for the largest and smallest values of a function on an interval?
8. In Example 4 in this section, we take the derivative of the function L. Do it yourself and explain which theorems from Section 3.1 you are using at each step.