In performing a line search for an objective function, F(X1, X2), presume that you have sampled the following three points: F1(-2, -2) = 11, F2(2, 6} = 10, and F3(3, 8) = 15. a. What is the search direction (expressed as a unit vector)? (Presume that F1 is the initial point of the line search) Note: W 3:0 to x1 D \"th0 x1\" b. Is the minimum bracketed? Why or why not? c. Use a 3-point quadratic polynomial approximation to estimate the location of the minimum along this line. i. Knowing starting point (2,-2) and search direction (part a) 4. 5'1: 1. Calculate (12 that yields x1 = [g] 2. Calculate 0L3 that yields x2 = [E33] ii. Solve for the coefficients of your quadratic approximation (b0, b1, and b2) iii. What is the value of (1*? iv. What are the corresponding [X1', X2'] values of the minimum along this search direction