Determine Whether the Vector Field Is Conservative $\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$

Multiple Choice

Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
$\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$

A) conservative with potential function $f ( x , y , z ) = x ^ { 10 } y$
B) conservative with potential function $f ( x , y , z ) = x y ^ { 10 }$
C) conservative with potential function $f ( x , y , z ) = x ^ { 11 } y$
D) conservative with potential function $f ( x , y , z ) = x y ^ { 11 }$
E) not conservative