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3. {18 marks) Find all critical points and classify each of them for the function xvxmxa) = x1 + 2x; + x2353 3x13 17% x3. 4. (13 marks) Apply method of steepest descent to estimate local minimum of the mction filmy) =x2 2xy+oy3 2x with initial point (xmyu) = (1,1). Do one iteration and determine (1:1,)?1). Express the nal answers for x1 and y1 as fractions. 5. {18 marks) Use method of Lagrange multipliers with the height function to determine the coordinates of the LOWEST point of the intersection of the plane x+y+z=1 and the sphere x2 + y2 + a2 = 1 in 3-dimensional space. 6. {16 marks) Given a quadratic function f(x,y) = 111:2 + My + c393 2m: where ml: and c are constants such that b2 4a: at 0. Determine the recursive formula in the Newton's method. You must show detailed calculations and simplify the