Determine Whether or Not the Vector Field $\mathbf { F } ( x , y , z ) = z \mathbf { i } + 2 y z \mathbf { j } + \left( x + y ^ { 2 } \right) \mathbf { k }$

Essay

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