Answer
See the explanation below.
Work Step by Step
a)
A conservative field is known to be a vector field which is the gradient of a scalar function (also known as a scalar potential function). It does not depend on the path. Mathematically, it can be shown as: $\nabla f=F$
b)
From part (a), we have $\nabla f=F$
Here, the potential function for a conservative vector field $F$ is a function $f$.
