# Math Help - Stationary Points - more?

1. ## Stationary Points - more?

Find and classify the stationary points:

$f(x,y)=xy+x^{-1}+y^{-2}$

$f_x=y-x^{-2}$

$f_y=x-y^{-2}$

$f_x=0\Rightarrow y-\frac{1}{x^2}=0$

$f_y=0\Rightarrow x-\frac{1}{y^2}=0$

Is $(1,1)$ the only stationary point?

Can $(0,0)$ be a stationary point?

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