Question

f(x,y)= x^2-y^2+xy-10x+3

Answer 1

what's the question?

Answer 2

to find critical point and also to determent max, min or saddle point..???

Answer 3

\[f(x,y)= x^2-y^2+xy-10x+3\]
\[f'_x(x,y)= 2x+y-10=0\]
\[f'_y(x,y)= -2y+x=0\]
\[\rightarrow x=4,y=2\]
\[f''_x(x,y)= 2,f''_y(x,y)= -2\]\[f''_{xy}(x,y)=f''_{yx}(x,y)=1\]
\[Hessian=-2*2-1=-5\]
(4,2) is saddle point