Find the Critical Points Of $f ( x , y ) = x ^ { 2 } y e ^ { - \left( x ^ { 2 } + 9 y ^ { 2 } \right) }$

Essay

Find the critical points of $f ( x , y ) = x ^ { 2 } y e ^ { - \left( x ^ { 2 } + 9 y ^ { 2 } \right) }$ Do this by setting $t = - \left( x ^ { 2 } + 9 y ^ { 2 } \right)$ and optimizing $f ( x , y , t ) = x ^ { 2 } y e ^ { t }$ subject to the constraint $t + x ^ { 2 } + 9 y ^ { 2 } = 0$