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Lagrange Multipliers - Temperature of a plate

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A thin plate occupies the region x^2/4 + y^2/9 is less than or equal to 1. If the temerature of the plate is T(x,y)= x^2 + y^2 - 5y + 5, find the coldest and hottest points on the plate.

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The coldest and hottest points on the plates are determined. Neat and step-by-step solution to the question.

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T(x, y) = x^2 + y^2 - 5y + 5

T'(x) = 2x

T'(y) = 2y - 5

T'(x) = 0 and T'(y) = 0 together imply that x = 0, y = 5/2

The point (0, 5/2) is the interior of the region x^2 /4 + y^2 /9 = 1 is a critical point.

The temperature at this point ...

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