I know that a conservative vector field means that the field vector, $F$, is equal to $\nabla\,f.$

So this means that $\nabla$f would be the potential function of $F$ if I'm correct.

So I tried to take the partial derivative of each component with respect to $x, y$ and $z$ and got:

$\nabla$f = $\langle\,2y, 0, 0\,\rangle$ 

I believe I messed up in the above step but have no idea how to get the answer from this.

The options for the answers are:

i) $x^2 yz$

ii) $x^2 y + yz - 87$ 

iii) $x^6 yz$ 

iv) $x^2 y +yz + z$ 

v) $\langle\,x^2 y, yz, z\,\rangle$