15. 16. 17. Let :1: and y be positive numbers such that 22: + 3y = 5 and f (3:, y) = (.7: 3) (y + 2) is optimized. Solve this (a) by substitution / optimization and (b) by using Lagrange multipliers. Does this point produce a maximum or minimum value for f? Consider the dierential du = (5519'2 + 2:12) (13.: + (3:23; + 23;) (lg. Calculate the line integral f0 do. where C is the line joining the point (2, 2) to the point (2, 2). Repeat the previous problem but now 0' is taken as the straight line segments from (2, 2) to (2,2) to (2, 2) Explain why the value of this integral matches the value in the previous