Provide an Appropriate Response $P _ { 0 }$ $f ( x , y ) = x y ^ { 2 } - y x ^ { 2 } , P _ { 0 } ( - 1,1 )$

Multiple Choice

Provide an appropriate response.
-Find the direction in which the function is increasing most rapidly at the point $P _ { 0 }$ .
$f ( x , y ) = x y ^ { 2 } - y x ^ { 2 } , P _ { 0 } ( - 1,1 )$

A) $\left( \frac { 1 } { \sqrt { 2 } } \right) \mathrm { i } - \left( \frac { 1 } { \sqrt { 2 } } \right) j$
B) $\left( \frac { 1 } { \sqrt { 2 } } \right) i + \left( \frac { 1 } { \sqrt { 2 } } \right) j$
C) $\left( - \frac { 1 } { \sqrt { 2 } } \right) \mathrm { i } + \left( \frac { 1 } { \sqrt { 2 } } \right) \mathrm { j }$
D) $( 1 \sqrt { 2 } ) \mathrm { i } - ( 1 \sqrt { 2 } ) \mathrm { j }$