Approximate f'(1) for f(x) = cos(x) using a centered difference. In Matlab, create an array called h. Start with h(1) = 0.05. In a while loop, decrease the step size by a factor of 2 each time until h(i) is smaller than 10^13 . Build another array in the same loop for the exact error in the approximation. Create a log-log plot of the results with the command: loglog(h,err). The plot should show an h which minimizes the error. From your plot, estimate the optimal h. Turn in this answer along with the plot.