(Second Order Methods)

(a) Unlike first order methods Second Order methods also make use of the second derivative of a function where possible. Explain what the second derivative represents and outline how this can be used to help converge on an optimum quicker than a first order method. (6 marks)

(b) Given the function f(x) = x³ 2x² + 1 and an x₁ of 3 calculate the first three iterations of Newtons Method. All calculations must be rounded to four digits of precision. (14 marks)