Chapter 18, Problem 8P

The following data come from a table that was measured with high precision. Use the best numerical method (for this type of problem to determine y at $x=3.5$. Note that a polynomial will yield an exact value. Your solution should prove that your result is exact.

x	0	1.8	5	6	8.2	9.2	12
y	26	16.415	5.375	3.5	2.015	2.54	8