please review the question below

4. Find the gradient and Hessian of each of the following functions and use the Hessians to check whether the functions are convex. (a) f : R2 -> R given by f(x1, X2) = (21 - 22)2 + 2x1. (b) f : Rd -+ R given by f(x) = (a, x)2 + (b, x), where a, b E Rd. Remark: Notice that part (a) is a specific example of part (b), with d = 2. (c) f : R3 -+ R given by f(x1, X2, 23) = 2cos(x1) + 202x3 (you may use a computer to find the eigenvalues of the hessian). 5. What is the direction of maximal increase, at the origin, of each of the three functions in Exercise 4 above