Chapter 18, Problem 9P

Use Newton's interpolating polynomial to determine y at $x=3.5$ to the best possible accuracy. Compute the finite divided differences as in Fig. 18.5 and order your points to attain optimal accuracy and convergence.

x	0	1	2.5	3	4.5	5	6
y	2	5.4375	7.3516	7.5625	8.4453	9.1875	12