Consider the polynomial function $f(x,y)=x^2{y}^2+x^{2}y+x{y}^2.$

$a.[3$ points$]$ Find all critical points $of$ the function.

$b.[2$ points$]$ Use the Second Derivatives Test $to$ classify each critical point $as$ the location $of$ either a local

maximum, local minimum, $or$ saddle point. $If$ the test $is$ inconclusive, then explain why.

Referring again $to$ the function $f(x,y)=x^2{y}^2+x^{2}y+x{y}^2$ from the previous question, find its $absolute$ maximum

and minimum values $on$ the square $[-2,1][-2,1].(You$ may refer $to$ your previous results without reworking them.$)$