(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