Questions 1] [30} Find derivative of the following functions [show your work): 2% E Br's a} z=2x3+3xy2+2y2,x=r2-32,y=r2+s b] |fw = eX+F+Z(x2 + y2 + 22), where X = (1' - s)2,y = (1' + 5)2:2 : dz (S - 1:02, evaluate E when I' = l and S = 1. 2] [3D] Solve questions below bv Langrange method. a} A firm manufactures a good from two raw materials, X and Y. The quantity of its good which is produced from X units ofX and 5! units on is given bv (10:, y) = x1!\" \"vs/4 If the firm spends $1280 each week on the raw materials, what is its maximum possible weeklv production, given that one unit ofX costs $16 and one unit on costs 51? b] Ev maximizing and minimizing x2 + y2 subject to the constraint x2 + X); + 3'2 =3, Find the minimum and maximum distances from the origin to the ellipse with equation x2 + X3! -l- y2 = . 3} (20) Find the area of the region bounded by the curves )1 = 2% and y = 2X 1n x+4 4} (20) Graph y = m