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

Arefrigeration system at your company uses temperature sensors fixed to read celsius (°c) values, but the system operators in your control room understand only the fahrenheit scale. you have been asked to make a fahrenheit (°f) label for the high temperature alarm, which is set to ring whenever the system temperature rises above –10°c. what fahrenheit value should you write on the label?