a VBA function doing the derivative and integral of a function

Derivative or Integral Of A Function (a) The derivative of the function f(x) at x = c is defined as f′(x)=lim f(c+h)− f(c)/h One way to attempt an estimate of f ′(c) is to choose a positive value of h that is as close to zero as Visual Basic allows, and then to evaluate the quotient. Unfortunately, round-off errors can be very large. A better method is to evaluate the formula f (c + h)− f (c)/h for smaller and smaller values of h, until the difference between successive approximations falls below a predetermined level. Write a program to calculate the derivative of a polynomial of degree n expressed as anxn +an−1xn−1 +...a1x+a0 where the coefficients an, a n-1,...,a1 , and, a0 are real numbers, n is a nonnegative integer, and an is not equal to zero. The program should accept as input the degree and coefficients of the polynomial along with a real number, c, and calculate the slope of the function at c. use the same polynomial function and simpson rule to approximate the integral.