Consider the following function: f(11,82) = x + 4x112 + 2x Suppose we employ the gradient method to minimise f, considering an initial point 2(0) = (1,1) and step size 1 = 0.1. After performing two iterations, what will be the point ~(2) (i.e., the value of the two-dimensional variable x after two iterations)? a. (0.24, -0.04) O b. (0.8,-0.56) O c. (2.64, 3.16) Od (0.16, 0.16) Now, suppose that we employ Newton's method to solve this problem, considering the same initial point 20 = (1,1) with a fixed step size of 1 =1. Hint: 1 g] = Which of the following statements is correct? O a. After one step, the solution obtained is (0,0), which is a global optimum. The method, in theory, could have taken more steps to find the optimum of f. b. After one step, the solution obtained is (0,0), which is the global optimum. The method only takes one step because the quadratic approximation used in the Newton's method is exact for quadratic functions, such as f. O c. After one step, the solution obtained is (0,0), which is a local optimum, but not a global optimum. O d. After one step, the solution obtained is (2,0), which is not an optimum. Further iterations would be necessary to find the optimal solution