Determine Whether the Vector Field Is Conservative $\overrightarrow { \mathrm { F } } ( x , y ) = \frac { 3 y } { x } \hat { \mathbf { i } } - \frac { x ^ { 3 } } { y ^ { 3 } } \hat { \mathbf { j } }$

Multiple Choice

Determine whether the vector field is conservative. If it is, find a potential function for the vector field. $\overrightarrow { \mathrm { F } } ( x , y ) = \frac { 3 y } { x } \hat { \mathbf { i } } - \frac { x ^ { 3 } } { y ^ { 3 } } \hat { \mathbf { j } }$

A) conservative with potential function $f ( x , y ) = \frac { 3 x ^ { 3 } } { y }$
B) conservative with potential function $f ( x , y ) = \frac { x ^ { 3 } } { 3 y }$
C) conservative with potential function $f ( x , y ) = \frac { x ^ { 3 } } { 4 y }$
D) conservative with potential function $f ( x , y ) = \frac { 4 x ^ { 3 } } { y }$
E) not conservative