1. The problem statement, all variables and given/known data Find the abs min/max values of the function f(x,y) = e1-2x2-y2 on the closed and bounded region x2 + y2 <= 1 3. The attempt at a solution First I have to find the critical points Dfx = (-4x)e1-2x2-y2 Dfy = (-2y)e1-2x2-y2 Clearly e1-2x2-y2 cannot equal 0, therefore x=y=0, Critical point is (0,0) Now, my professor has done most of these problems by setting [tex]\nabla[/tex]f = [tex]\lambda[/tex][tex]\nabla[/tex]g, the gradients of each function Even with this method yields x=0 and y=0 to be the only solution. I am not too sure how to incorporate the bounded region into this question. Do I just look at x=0 and y=0 of x2 + y2 = 1? This would result in x2 + 0 = 1 x=y= +/- 1 giving me two points, (-1, -1), and (1,1), however f(-1,-1) > 1 and f(1,1) = e-2 thus a min/max value for the function? Is this correct? Any insight would be great, thanks.