Chapter 18, Problem 5P

Given these data

x	1.6	2	2.5	3.2	4	4.5
$f\left(x\right)$	2	8	14	15	8	2

(a) Calculate f (2.8) using Newton's interpolating polynomials of order 1 through 3. Choose the sequence of the points for your estimates to attain the best possible accuracy.

(b) Utilize Eq. (18.18) to estimate the error for each prediction.