Aflat circular plate has the shape of the region x^2 + y^2 ≤ 1. the plate, including the boundary where x^2 + y^2 = 1, is heated so that the temperature at the point (x, y ) is t (x, y) = x^2 + 2 y^2 − x. find the temperatures and locations of the hottest and coldest points on the plate. solve this as a maximum/minimum problem, not as a lagrange multiplier problem