For the function f2 on p. 161 of Lyche et al. Write a code to construct the C and C cubic interpolating splines with 3, 7, 15, and 31 interior nodes. Submit one plot for each number of interior nodes. Each plot must contain f2 and both interpolating splines. Additionally, submit the lists of the Bernstein coefficients for the case of 3 interior nodes for each spline. Modify your code to compute the numerical error of approximation for both C and C cubic interpolating splines. Derive the nu- merical order of convergence and compare it with the theoretical one. cubic C splines: 6, 7, 11 and 16 nodes, Lyche et. al, p. 161 0.9 0.8 0.7 0.6 0.5 0,4 0.3 0.2 0.1 0 -5 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 5 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -6 0.9 0.8 0,7 0.6 0.5 0.4 0.3 0.2 0.1