2. (U: 20pts, G: 20pts) Consider the problem min f (x) = (1 + 2x2 - 7)2+ (21 + 202 -5)2 . a. 8pts. Calculate the gradient and the Hessian of this function . b. 8pts. Use the necessary conditions for unconstrained opti- mization to find a candidate minimizer of this function. . c. 4pts. Use the sufficient conditions to verify whether or not the point is a minimum. For the previous parts, no computer should be used, except in part c it may be used to find eigenvalues. 3. (U: 20pts, G: 15pts) In a programming language of your choice, im- plement either gradient descent or Newton's method to numerically solve the previous problem. Include comments in your code pointing out your step size choice and your stopping condition choice. For x* the exact answer derived in the previous problem, and x the numeri- cal answer your code provides, refine your code such that your answer satisfies If (x*) - f(x) |