6. (a) A Powell's method algorithm has used the following search directions in the first six line searches: [1, 0], [0, 1], [1, 2], [0, 1], [1, 2], [1, 3]. What should the seventh (next) search direction be? Do not consider "resetting" directions to the univariate directions. (b) While performing a line search for a 2-dimensional objective function, presume that you have sampled the following three points: F([2, -2]) 12, F([2, 6]) 10, and F([3, 8]) 15. Use a 3-point quadratic polynomial approximation to estimate the location of the minimum along this line. What are the Di,X values of the minimum along this search direction? 6. (a) A Powell's method algorithm has used the following search directions in the first six line searches: [1, 0], [0, 1], [1, 2], [0, 1], [1, 2], [1, 3]. What should the seventh (next) search direction be? Do not consider "resetting" directions to the univariate directions. (b) While performing a line search for a 2-dimensional objective function, presume that you have sampled the following three points: F([2, -2]) 12, F([2, 6]) 10, and F([3, 8]) 15. Use a 3-point quadratic polynomial approximation to estimate the location of the minimum along this line. What are the Di,X values of the minimum along this search direction