You are looking for the highest and lowest possible z coordinates of points {x, y, z} on a the level surface f[x, y, z] = 1 for a function f[x, y, z].

Explain the following

At {x1, y1, z1}on the level surface with the highest z or the lowest z coordinate, the first two slots of gradf[x1, y1, z1]must be 0.