(a) Let us take the interval [1,e] as our basic domain. First, determine how many data points, chosen to correspond with Chebyshev roots, you would need in order to ensure 10 decimal places of accuracy on [1,e]. Make sure to verify your answer. This will require you to come up with the formula for the nth derivative of f(x) = ln x.

(b) Using MATLAB, create a function which takes as its input any value x from [ and generates an approximation of In a as its output. Your program should make use of Newton's divided difference scheme to find the coefficients for the interpolating polynomial which passes through the proper number of (Chebyshev) data points to ensure the accuracy discussed in part (a). Nested multiplication will also be required in order to evaluate this polynomial