Can the potential function have a maximum or minimum is free space ?

Explanation

In free space, there is no charge present but it cannot be said that the electric field is zero. As we know the relation between the electric field intensity and the potential,
`E=(dV)/(dr)`
In order to have maximum or minimum value of potential:
`(dV)/(dr)=0 or, E=0` (for the point of maxima or minima)
If suppose there is no electric field in free space then potential will remain constant and we cannot talk about maxima or minima.
If suppose electric field is non-zero in free space then it cannot be zero at a point specifically, because electric lines are supposed to be continuous in free space as there are no charges present. Electric lines can start or end at the charge but in absence of charge lines must continue indefinitely. Therefore, the potential function cannot have the maximum or minimum value in free space.