1.7. (a) Write a program to compute an approx- imate value for the derivative of a function using the finite-difference formula Test your program using the function tan(x) for x = 1, Determine the error by comparing with the square of the built-in function sec(x). Plot the magnitude of the error as a function of h, for h = 10-K, k = 0, . . . , 16, You should use 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 h ~ Vmach derived in Example 1.3? (b) Repeat the exercise using the centered differ- ence approximation