Determine Whether $\mathbf { F }$ Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

Multiple Choice

Determine whether $\mathbf { F }$ is conservative. If so, find a function $f$ such that $\mathbf { F } = \nabla f$ .
Select the correct answer.
$$\mathbf { F } ( x , y ) = \left( 5 x ^ { 4 } + 4 y \right) \mathbf { i } + \left( 7 x - 5 y ^ { 4 } \right) \mathbf { j }$$

A) $f ( x , y ) = 5 x ^ { 4 } + 4 y + 7 x - 5 y ^ { 4 } + C$
B) not conservative
C) $f ( x , y ) = x ^ { 5 } + y ^ { 5 } + C$
D) $f ( x , y ) = x ^ { 5 } + 4 y ^ { 2 } + 7 x ^ { 2 } - y ^ { 5 } + C$ .