Assignment 4 -Numerical Analysis for scientists

1. (a) (6 marks) Find the Taylor polynomial of degree 3 for f(x) = x^(3/2) expanded
about x0 = 4.
(b) (2 marks) Does f(x) =x^(3/2) have a Taylor polynomial expansion about x0 = 0?
Justify your answer.

2. Consider the data
(a) (5 marks) Find an interpolation polynomial of degree 4 by solving the system
AX = B (Use Matlab to solve the system AX = B).
(b) (3 marks) Use Matlab built in functions to find an interpolation polynomial of
degree 4 and then to approximate the value at x = -1.4.