APPM 2350 Midterm: appm2350summer2016exam2_sol
Document Summary
Summer 2016: (15 pts) a at circular plate has the shape of the region x2+y2 1. The plate, including the boundary where x2+y2 = 1, is heated so that the temperature at the point (x, y) is t (x, y) = x2 + 2y2 x. Find the temperatures and locations of the hottest and coldest points on the plate. The function t (x, y) = x2 + 2y2 x is a polynomial and continuous throughout r2, thus is continuous on the unit disk. The region containing the plate is the unit disk and thus is a closed, bounded region. We begin by nding the critical points of t by taking the partial derivatives and setting them to 0. = 2x 1 = 0 = x = = 4y = 0 = y = 0 bounded intervals. 2 , 0(cid:1), which lies inside the unit disk.
