True of false about partial derivative

[zhuyilun]

Homework Statement

if (2,1) is a critical point of f and f_xx(2,1)f_yy(2,1) < (f_xy(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?

 

[lanedance]

wouldn't it need f_x(2,1) = f_y(2,1) = 0 as well?

 

[zhuyilun]

wouldn't it need f_x(2,1) = f_y(2,1) = 0 as well?

could you please explain it a little bit more?

 

[lanedance]

ok now i see it is already a critical point, i would agree with you then