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 . (2) 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 the magnitude of the error. Is there a minimum value for the magnitude of the error? b) (5 points) Check if the corresponding value of h to the minimum value for the magnitude of the error can be approximately equal to eps ? Why?