I need solve this assignment of calculus III. MA261

Work Problem (60 points) You must prow'de a clear and detailed solution for each question using the material of chapters: 14.6, 14. 7, 14.8, 15.1, and 15.2 only Question 1 [20 pts] Given the function of two variables f(x, y) = 4x3 60x2 +12xy2 24y2 + 3. a) [10 ptsl Find and classify all critical points of the function f (x, y). b) [10 pts] Find a vector I: such that the directional derivative of the function f (x, y) at the point (1, 4) in the direction of u is equal to 361/145. Question 2 [20 pts] Given the function of two variables f(x,y) = 5x2 2xy 8y2 8. a) [10 pts] Use Lagrange Multipliers to nd the extreme value(s) of the function f subject to the constraint 4x + y 4 = O. b) [10 pts] Verify that f(x, y) = (5x + y)2 (3?9y2 + 8) and show that f has maximum and no minimum with the constraint 4x + y 4 = 0. Question 3 [20 pts] Given the region D enclosed by y2 = x2 andxz + (y 8)2 = 32. a) [10 pts] Set up the double integral that represents the area of the region D. b) [10 pts] Evaluate the area of the region D