Use the Newton backward-difference formula to construct interpolating polynomials of degree one, two, and three for the following data. Approximate the specified value using each of the polynomials.
a. f (−1/3) if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750, f (0) = 1.10100000
b. f (0.25) if f (0.1) = −0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) = 0.24842440