Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f{x,y) at each of these points. Ifthe second-derivative test is inconclusive, so state. f(x,y) = 9x2 + 18xy y3 + 81y; ( 3, 3), (9,9) i:__Z' A. f(x,y) has a relative minimum at ( 3, 3}. r" _;. B. f(x,y) has neither a relative maximum nor a relative minimum at (3, 3). ii} (3. for, ) has a relative maximum at ( 3, 3). i' _;. D. The second-derivative test is inconclusive at ( 3, 3). What is the nature of the function at (9,9)? (:3 A. f(x,y) has a relative maximum at (9,9). Vi: B. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). C: C. f(x, ) has a relative minimum at (9,9). C: D. The second-derivative test is inconclusive at (9,9). Find the dimensions of an open rectangular glass tank of volume 864 cubic feet for which the amount of material needed to construct the tank is minimized. x: 12 feet y: 12 feet Z: 12 feet Afarmer can produce f(x.y) = 2311|ll5x2 + y2 units of produce by utilizing x units of labor and y units of capital. (a) Calculate the marginal productivities of labor and capital when x = 9 and y: 6. (b) Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 9 to 9 + h units while keeping capital fixed at 6 units. (c) Use part (b) to estimate the change in production when labor decreases from 9 to 7.5 units and capital stays fixed at 6 units. (a) The marginal productivity of labor when x: 9 and y = 6 is 495 . (Simplify your answer.) The marginal productivity of capital when x = 9 and y: 6 is 66 . (Simplify your answer.) (b) Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 9 to 9 + h units while keeping capital fixed at 6 units. Production will change approximately 495 units. (c) Use part (b) to estimate the change in production when labor decreases from 9 to 7.5 units and capital stays fixed at 6 units. The production will decrease approximately 742.5 units