Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 2.3

1. What does it mean for f' to ``change sign'' at the points A' and C'? Look carefully at the graphs on page 119.
2. The book calls point B an ``inflection point.'' What does this mean? What does it mean to say that the ``direction of concavity changes?'' Use your own words and examine the graphs on page 119 closely.
3. What is the relationship between the derivative of f and the increasing or decreasing of f?
4. How does example 1 show that the statement ``if f is increasing at x = a, then f'(a) > 0'' is false? Write down the correct statement.
5. What is the difference between a point and a value?
6. What is a local maximum point of a function? How can you find one?
7. In example 2, what was the key difference between the points x = - 1 and x = 0? Explain how we could use the graph of the derivative to find where the function is maximum, minimum, or just flat.
8. Explain the first derivative test.
9. How are the inflection points of f and the derivative of f related?