to Solutions Homework Assignment 29
MATH 345-01 Section 50, Page 171 8 8. u(x, y) = z = ex cos y. Thus ux = ex cos y and uy = ex sin y. These are never simultaneously zero, so u has no critical points. On the boundary of the region, we have four curves to consider. (a) x = 0 : u(x, y) = cos y, which has a max of 1 at y = 0 and a min of 1 y at = . (b) x = 1 : u(x, y) = e cos y, which has a max of e at y = 0 and a min of e at y = . (c) y = 0 : u(x, y) = ex , which has a max of e at x = 1 and a min of 1 at x = 0. (d) y = : u(x, y) = ex , wh...