relative maxima,relative minima, saddle?

Question

how to find relative maxima,relative minima, saddle point of f(x,y)=x^2-9xy+y^2

what i only know is
partial of f w.r.t x= 3x^2-9y
and partial of f w.r.t y =3y2-9x

Answer 1

First put partial derivatives to zero

2x-9y=0 and -9x+2y=0 The only solution is (0,0)

To find out what happens at this point you must calculate
H = f_xx*f_yy -f^2_xy and study its sign combined with the sign of
f_xx

Answer 2

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