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###### Find the absolute maximum and minimum values of f on D. (a) f(x,y) = x2+y2 2x; D is the closed triangular region with vertices (2,0), (0,2), and (0,-2)_ Answer: max: f(0,+2) = 4; min: f(1,0) = -1 (b) f(x,Y) = 4x?+Y; D = {(X,y)lx? +y2 < 1} Answer: max: f(+1,0) 4; min: f(0,0) = 0 Find three positive numbers whose sum is 60 and whose product is maximum Hint: The problem can read: max *YZ , subject to (xY,zi Thus for example it can be reformulated a5; maxxy(60 ~y) KY with each component being pos

Find the absolute maximum and minimum values of f on D. (a) f(x,y) = x2+y2 2x; D is the closed triangular region with vertices (2,0), (0,2), and (0,-2)_ Answer: max: f(0,+2) = 4; min: f(1,0) = -1 (b) f(x,Y) = 4x?+Y; D = {(X,y)lx? +y2 < 1} Answer: max: f(+1,0) 4; min: f(0,0) = 0 Find three positive numbers whose sum is 60 and whose product is maximum Hint: The problem can read: max *YZ , subject to (xY,zi Thus for example it can be reformulated a5; maxxy(60 ~y) KY with each component being positive. From this; You may conclude x Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane 2x Sy 30. Clue: Try to use the hint given for Problem 14.81.

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