2 Employ inverse interpolation using a cubic interpolating p

2) Employ inverse interpolation using a cubic interpolating polynomial and bisection to determine the value of x that corresponds to f(x) = 1.7 for the following tabulated data.

Solution

The following points are used to generate a cubic interpolating polynomial

x₀ = 1         f(x₀) = 3.6

x₁ = 2         f(x₁) = 1.8

x₂ = 3         f(x₂) = 1.2

x₃ = 4         f(x₃) = 0.9

The polynomial can be generated in a number of ways including Newton