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

Determine whether F is conservative. If so, find a function f such that $\mathbf { F } = \nabla f$ . $\mathbf { F } ( x , y ) = \left( 4 x ^ { 3 } + 2 y \right) \mathbf { i } + \left( 3 x - 4 y ^ { 3 } \right) \mathbf { j }$

A) $f ( x , y ) = x ^ { 4 } + 2 y ^ { 2 } + 3 x ^ { 2 } - y ^ { 4 } + C$
B) not conservative
C) $f ( x , y ) = x ^ { 4 } + y ^ { 4 } + C$
D) $f ( x , y ) = 4 x ^ { 3 } + 2 y + 3 x - 4 y ^ { 3 } + C$

Correct Answer:

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