We normally consider the gravitational force of the earth on an object of mass m to be given by the constant F = - g mk, but, of course, this is valid only in regions near the earth's surface. Find the potential function f for F and use it to show that the work done by F when an object is moved from (x1, y1, z1) to a nearby point (x2, y2, z2) is mg (z1 - z2).