Write a (C++, Python, or Java) 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 cos(x) for x = 0, / 2 , , 3/ 2 , 2.

Determine the error by comparing with the built-in function sin(x).

Plot the magnitude of the error as a function of h, for h = 1 2 , 1 4 , 1 8 , . . . . Use a log scale for h and the magnitude of the error.

Is there a minimum value for the magnitude of the error?