If f(x,y)= xy+(1/x)+(1/y)(adsbygoogle = window.adsbygoogle || []).push({});

I find that f_{x}= y-(1/x^{2})=0 and f_{y}=x-(1/y^{2})=0.

Solving for coordinates x and y by substituting the equations, I find that y=0 or 1. However, if i try to solve for x-coordinates with y=0, I get an infinity. So does that mean I ignore the possibility of y=0?

Another question is with second-derivative test where D=f_{xx}*f_{yy}-f_{xy}^{2}.

I know that if D>0 and f_{xx}<0, then it is a local max. But what if I was told D>0 and given only f_{yy}<0 and was to determine if it's a local max or min. Could I make the same argument with only f_{yy}<0 that it is a local max?

Thanks a lot

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# Second derivatives and local max/min

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