Determine whether or not $\mathbf { F } ( x , y ) = \left( 3 x ^ { 2 } - 4 y \right) \mathbf { i } + \left( 4 y ^ { 2 } - 2 x \right) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$ .

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The Answer of Determine whether or not $\mathbf { F } ( x , y ) = \left( 3 x ^ { 2 } - 4 y \right) \mathbf { i } + \left( 4 y ^ { 2 } - 2 x \right) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$ .

Determine Whether or Not F(x,y)=(3x2−4y)i+(4y2−2x)j\mathbf { F } ( x , y ) = \left( 3 x ^ { 2 } - 4 y \right) \mathbf { i } + \left( 4 y ^ { 2 } - 2 x \right) \mathbf { j }F(x,y)=(3x2−4y)i+(4y2−2x)j

Determine Whether or Not $\mathbf { F } ( x , y ) = \left( 3 x ^ { 2 } - 4 y \right) \mathbf { i } + \left( 4 y ^ { 2 } - 2 x \right) \mathbf { j }$