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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.