Another Approximation Technique - Newton's Method

Newton's Method is an algorithm for finding the root of an arbitrary polynomial:

                  n            n-1                 1
     f(x) = Cn * x   + Cn-1 * x     + ...  + C1 * x   + C0

The idea is to make a guess of what the root is and testing if f(guess) = 0. If not, we improve the guess, and try again. The formula for improving the guess is:


                          f(guess)
     new guess = guess - ----------
                          f'(guess)

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