Find All Points (X, Y) Where $f ( x , y ) = \frac { 1 } { x } + x y - \frac { 1 } { y }$

Multiple Choice

Find all points (x, y) where $f ( x , y ) = \frac { 1 } { x } + x y - \frac { 1 } { y }$ has a possible relative maximum or minimum. Use the second-derivative test to determine, if possible, the nature of f(x, y) at each of these points.

A) (1, 1) gives a relative minimum point
B) (-1, 1) gives a relative maximum point
C) (-1, 1) gives a relative minimum point
D) Neither a relative maximum nor a relative minimum at (-1, 1)