1. The problem statement, all variables and given/known data The temperature at a point (x, y) on a metal plate is T(x, y) = 4x^2 − 4xy + y^2 . An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. Using the method of Lagrange multipliers, find the highest and lowest temperatures encountered by the ant. 2. Relevant equations 3. The attempt at a solution T(x,y) = 4x^2 − 4xy + y^2 gradient of T = (8x - 4y)i + (2y - 4x)j g(x,y) = x^2 + y^2 = 5^2 gradient of g = (2x)i + (2y)j gradient of T = (lambda)gradient of g ----> lambda=# 8x - 4y = #2x ---->1 2y - 4x = #2y ---->2 # = 4-4y = 1-4x what am i going to do next?