Question

find the absolute max/min of f(x,y) = e^(-x^2-y^2) * (x^2+y^2) on D = x^2+y^2<4

Answer 1

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Answer 2

Alright, I can't do all the work typing but what you want to do is take the partial of f(x,y) with respect to x and y and set them BOTH to zero. Find the x and y values or the critical points. Next, you want to take your domain D and solve it for x or y, substitute it back in and redifferentiate it with respect to x and y. Find the critical points. Since your region is a circle there are no "corner" points. Then, to test them, use the Hessian, or discriminant, which is \[f_{xx}f_{yy}-(f_{xy})^2\]. If it is negative then it is a saddle point. If it is positive you need to check the second partial with respect to x,\[f_{xx}\]. If it is positive that means it is concave UP and the point is an absolute MIN. If it is negative then it is concave DOWN and is an absolute MAX. Tell me if you need any help!

Answer 3

thanks alot..when I took the two partials and solved the system I got the points (0,0) and (1,0). I just wanted to check if I took the partials right

Answer 4

got it thanks