5. Determine the values of the parameter a for which the function f(x,y) = -6x + (2a + 4)xy y2 + 4ay is a) convex b) concave on R2 6. Find all local maxima, local minima and saddle points for a) f(x) = x? e-* b) f(x1,x2) = x2 3x2x3 + x c) f(x1, x2) = X1X2 + X2*3 + X X3 7. Consider the minimization problem 1 min f(x) = (x - 1)2 + (logx-273 s.t. x [1.5, 4.5). a) Estimate the number of function evaluations needed for the Golden Section method to reduce the size of interval to be less or equal to 0.2. (Do not carry out actual computation.) b) Use the Golden Section algorithm to find an approximate minimum and minimizer of the problem. (Stop if the interval size is reduced to be less or equal to 0.2). 8. Use the method of steepest ascent to approximate the optimal solution to the following problem with the initial point (2.5, 1.5) max z = -(x - 2)2 - *, x You can stop after 10" iteration if stopping conditions are not satisfied. Show your work properly in a tableau format