# 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&prime;(x)=lim f(c+h)&minus; f(c)/h

One way to attempt an estimate of f &prime;(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)&minus; 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&minus;1xn&minus;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.

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Project ID: #4411271

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