Question

Find local minimum and maximum value of the function (x^2 + y^2)*Exp(-x^2 - y^2).

Answer 1

So I got the first partial derivates of the function since they have to be equal to 0

Answer 2

then you have to calculate the hesse matrix and if its >0 then local max, if <0 its local min

Answer 3

but I got a solution that gives\[x=\sqrt{1-y^2}\] and I dont know why there couldnt be a max or min point in these solutions.

Answer 4

actually your function as you found has a maximum at all the points on the circll
\( x^2 +y^2 =1\) and a minimum at (0,0)