1. The problem statement, all variables and given/known data
Consider the function f(x,y) = (x2 + 4y2)e(1-x2-y2)
Find all critical points, and identify them as maxima, minima, or saddle points.
3. The attempt at a solution
I took the partial of x and the partial of y, and set them equal to 0. This is what I got:
fx(x,y) = 4y2 - x2 - 1 = 0
fy(x,y) = 4y - 2x2 + 4 = 0
But from here I'm kind of lost. I took Calc 3 a year ago, last fall, and now I've had to recall a lot of it for my PChem class. This is one of our homework questions, and I'm just having a lot of trouble remembering what the steps are for this. Help is greatly appreciated. Thanks!
Consider the function f(x,y) = (x2 + 4y2)e(1-x2-y2)
Find all critical points, and identify them as maxima, minima, or saddle points.
3. The attempt at a solution
I took the partial of x and the partial of y, and set them equal to 0. This is what I got:
fx(x,y) = 4y2 - x2 - 1 = 0
fy(x,y) = 4y - 2x2 + 4 = 0
But from here I'm kind of lost. I took Calc 3 a year ago, last fall, and now I've had to recall a lot of it for my PChem class. This is one of our homework questions, and I'm just having a lot of trouble remembering what the steps are for this. Help is greatly appreciated. Thanks!
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