Question

Find f(2.8) from the following table.

x	0	1	2	3
f(x)	1	2	11	34

Answer 1

To find y = f(x) at x = 2.8 from the given table. 

We use Newton’s backward interpolation formula since the required value is near the end of the table.

2.8 = 3 + (n)1

n = 2.8 – 3 = -0.2 

The difference table given below

y = 34 – 4.6 – 1.12 – 0.288

y = 27.992 

Hence the value of f(x) at x = 2.8 is 27.992