I have to find the critical points of a function f, and verify they are saddle points(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(x,y) =\left\{\begin{array}{cc}e^{\frac {1} {x^2*y}},&\mbox{ if }x*y\neq 0\\0, & \mbox{x*y=0}\end{array}\right[/tex].

I found that the partial derivatives are 0 only on the axis, where f(x,y) is equal to 0, and i know that for every point outside the axis f(x,y)>0. My question is if the axis are saddle points and why????.

Any help would be much appreciated.

Regards, Paul.

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# Saddle points

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