Suppose $(1,4)is$ a critical point $of$ a function $f$ with continuous second derivatives. Calculate the value $of$ the determinant $D,$ and use the second derivative test $to$ determine the

nature $of$ the critical point $in$ each $of$ the following cases.

$(a)f_{}(1,4)=5,f_{xy}(1,4)=-1,f_{yy}(1,4)=4$

Saddle Point.

Local min.

Local max.

$No$ information.

$(b)f_{}(1,4)=-10,f_{xy}(1,4)=-1,f_{yy}(1,4)=-10$

Saddle Point.

Local min.

Local max.

$No$ information.