A discrete data set with x=0.75 steps is presented in the table. Obtain function values at x=0.25 steps using;

a)Lagrange interpolating polynomial.

b)Linear splines.

c)Quadratic splines.

d)Cubic splines.

Present your results in a table.

Then, plot your results. Which of these methods seem more suitable for given data? Briefly explain why.

x_i f_i

-3 0.1

-2.25 0.164948

-1.5 0.307692

-0.75 0.64

0 1

0.75 0.64

1.5 0.307692

2.25 0.164948

3 0.1