True of false about partial derivative

zhuyilun
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Homework Statement


if (2,1) is a critical point of f and fxx(2,1)fyy(2,1) < (fxy(2,1))^2
then f has a saddle point at (2,1)


Homework Equations





The Attempt at a Solution


i think its right
but it turns out to be wrong
can someone tell me why?
 
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wouldn't it need fx(2,1) = fy(2,1) = 0 as well?
 
lanedance said:
wouldn't it need fx(2,1) = fy(2,1) = 0 as well?

could you please explain it a little bit more?
 
ok now i see it is already a critical point, i would agree with you then
 

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