I need solve this assignment of calculus III. MA261

Question 1 [30 points] a. [15 points] Use the method of Lagrange multipliers to nd the extreme value(s) of f (x, y) = x y subject to the constraint x2+2y2=1 b. [5 points] For each of the extreme value(s) found in part (a) check if it is a maximum or a minimum. justify your response by calculations. c. [10 points] Compute the integral f [D ydydx , where 0 S x 5 7r, andO g y S sinx Question 2 [30 points] a. [15 points] Find the critical points of the function f(x, y) = 6x2 2x3 + 3y2 + 6xy. b. [15 points] Find the local maximum and minimum values and saddle points of the function f(x, y) = 6x2 - 2x3 + 3y2 + 6xy