In Exercises 3–17, determine whether the given vector field $\mathbf{F}$ is conservative. If it is, find a scalar potential function for $\mathbf{F}$. 9. $\mathbf{F} = (6xy^2 - 3x^2)\mathbf{i} + (y^2 + 6x^2y)\mathbf{j}$
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We check if $\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}$. $\frac{\partial P}{\partial y} = \frac{\partial}{\partial y}(6xy^2 - 3x^2) = 12xy$ $\frac{\partial Q}{\partial x} = \frac{\partial}{\partial x}(y^2 + 6x^2y) = 12xy$ Since $\frac{\partial Show more…
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