(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the absolute minimum and maximum values of f on the set D.

f(x,y)= e^{-x2-y2}(x^{2}+2y^{2}); D is the disk x^{2}+y^{2}<= 4

2. Relevant equations

Second Derivatives test,

partial derivatives

3. The attempt at a solution

f_{x}(x,y) = 0 = (e^{-x2-y2})(-2x) + (x^{2}+2y^{2})(-2x e^{-x2-y2})

f_{y}(x,y) = 0 = (e^{-x2-y2})(4y) + (x^{2}+2y^{2})(-2y e^{-x2-y2})

f_{xy}(x,y) = (e^{-x2-y2})+(-2x)(-2y e^{-x2-y2}) + (x^{2}+2y^{2})(-2x*-2y e^{-x2-y2}) + (-2x e^{-x2-y2})(4y)

f_{x}and f_{y}simplify to:

f_{x}(x,y) = 1+x^{2}+2y^{2}= 0

f_{y}(x,y) = -2y+x^{2}+2y^{2}= 0

I'm stymied here because the equation I get for f_{x}seems impossible to solve. Did I make a mistake differentiating?

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# Finding absolute minimum and maximum values

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