A flat 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