Second Order Methods)

(a) Show the structure of the 2D Hessian matrix. Explain what the Hessian matrix represents and determine what we know about our optimum when this matrix is positive definite or positive semi-definite

(b) Given the function f(x) = 2x3 5x2 + 1 and an x1 of 2 calculate the first three iterations of Newtons Method. All calculations must be rounded to four digits of precision