A metal plate has the shape of the region x2 + y2 ≤ 1. The plate is heated so that the temperature at any point (x, y) on it is indicated by
T (x, y) = 2x2 + y2 − y + 3.
Find the hottest and coldest points on the plate and the temperature at each of these points. (Hint: Parametrize the boundary of the plate in order to find any critical points there.)
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