1. Interpolation In this part, you investigate how the number of nodes in polynomial interpolation affects interplation error. The following Matlab m-function is provided on Canvas for download. Lagrange: An m-function which connstructs and evaluates an interpo- lating polynomial in Lagrange form; The output y of the m-function is the vector containing the values of the interpolating polynomial evaluated at the values in the input vector x. The data points are input to the m-function in the vectors xi and fi with the vector xi containing the nodes. Write a Matlab script interpolationError.m to do the follows for each value of n = 10 and n = 20. Use f(x) = sin(x) to generate (n+1) data points (Xi, Yi) (1