Find All the Critical Points of the Function $f ( x , y ) = x y + \frac { 8 } { x ^ { 2 } } + \frac { 8 } { y ^ { 2 } }$

Short Answer

Find all the critical points of the function $f ( x , y ) = x y + \frac { 8 } { x ^ { 2 } } + \frac { 8 } { y ^ { 2 } }$ Classify these critical points as local maxima, local minima, or saddle points.