10-11. Let f(x,y) = xy – 2x – 3y with triangular domain D whose vertices are (0,0),(4,0). and (4,8). (See diagram below.

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10 11 Let F X Y Xy 2x 3y With Triangular Domain D Whose Vertices Are 0 0 4 0 And 4 8 See Diagram Below 1 (28.14 KiB) Viewed 14 times

10-11. Let f(x,y) = xy – 2x – 3y with triangular domain D whose vertices are (0,0),(4,0). and (4,8). (See diagram below.) a) Calculate the gradient of f(x,y). b) Use the gradient to determine all critical points of the function in the interior of the domain. c) Parameterize the horizontal leg and determine the critical points of f for this leg. d) Parameterize the vertical leg* and determine the critical points of f for this leg. e) Parametrize the hypotenuse* and determine the critical points off for this leg. f) Evaluate f(x,y) at each of the points you found above. g) Explain how we know that both a maximum and minimum must exist. h) State the maximum and minimum value of f(x,y). (4.81 "Hint: Once you parametrize an edge, use those values to write f(x,y) as f(t) (0,0) (4,0)