Language: Matlab

Write a program to compute an approximate value for the derivative of a function using the finite-difference formula f'(x) f(x + h) - f(x)/h Test your program using the function sin(x) for x = 1. Determine the error by comparing with the built-in function cos(x). Plot the magnitude of the error as a function of h, for h = 1/2, 1/4, 1/8 ... You should use a log scale for h and for the magnitude of the error. Is there a minimum value for the magnitude of the error? How does the corresponding value for h compare with the rule of thumb Repeat the exercise using the centered difference approximation f' f(x + h) - f (x - h)/2h