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Mathematics, 27.11.2019 04:31 14onufriychukliliya
Use lagrange multipliers to prove that the rectangle with max area that has a given perimeter p is a square. let the sides of the rectangle be x and y and let f and g represent the area a and the perimeter p respectively. find the following. a = f(x, y) = xy; p = g(x, y) = 2x + 2y; grad f (x, y) = ? ; lambda grad g = ? then lambda = 1/2 y = x/2 implies that x = y; therefore the rectangle with max area is a square with side length ? i have answered most of these questions, but there are three that i seem to be having trouble with. i thought grad f = , but lambda grad g should be a vector as well, neither one of them worked. with explaination would be very much appreciated.
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