Question $14\mathrm{.}3$ Progress Check $2$

The Hessian for the function $f(x,y)=y^2-x^{2}at$ its

critical point $at$ the origin $is$ given $by$

$Hf(0,0)(h_1,h_2)=h_2^2-h_1^2$ and therefore the Hessian $is$

Thus, the function $f(x,y)=y^2-x^2$ has $a$

$at$ the origin.

Select your answer from the options listed. The first word $in$ each answer

choice fills $in$ the first answer blank, and the second word fills $in$ the

second answer blank.

positive$-$definite; saddle point

positive$-$definite; local minimum

positive$-$definite; local maximum

negative$-$definite; saddle point