Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 4.5

1. What would a linear spline be good for?
2. When will a linear spline have no corners?
3. In the picture ``Connecting Dots II'' on page 287, what are the endpoints of the pieces of parabolas pictured?
4. Hey look! The book is switching up the ``usual'' order of a, b and c when talking about quadratic functions.
5. Was there more than one choice for S₂ in Example 2?
6. Suppose that you need to complete Example 2 by connecting the knot at (5, 1) with another knot at (6, 3).
   1. We would need to first write S₅ in powers of (x - 5). How would you do that?
   2. Then, to solve for the a, b and c, we would need to come up with three conditions that S₅ would have to satisfy. Can you write down what they would be?
7. If f (t) is a function describing your positon while driving down the road, which of f, f', f'' are continuous?
8. Why might you want to use cubic splines instead of quadratic splines?