Recall the derivation of the Newton iteration formula discussed in the lecture; it was based on a Taylor series expansion of the function f(x) around an estimate of the root x^(k−1), truncated after the linear term. You are asked to derive a more accurate iteration scheme as follows: Start from the Taylor series expansion of f(x) around x^(k−1), and truncate it after the quadratic term; then derive a general iteration formula for x^(k), and explain how you would use it.