Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 2.5

1. Given two points P and Q on a curve, describe the ``secant line'' through those two points; i.e., what points does the secant line go through, what is the slope of the secant line, etc.
2. Explain the difference between a secant line and a tangent line.
3. Summarize, in your own words, the process of solving Example 3.
4. Review questions: If we let f (x) = x² + x, what is f (2 + h)? This would be a great time to review function notation and your algebra skills!
5. What is the difference between ``average'' velocity and ``instantaneous'' velocity?
6. What is the formal definition of the derivative of f at x = a?
7. Does the derivative at a point always exist?
8. What is the formula for a difference quotient?
9. What does the denominator of a difference quotient represent?
10. What does the numerator of a difference quotient represent?
11. What does the quotient represent?
12. How do we get from ``average'' rate of change (the difference quotient) to ``instantaneous'' rate of change (the derivative)?