Let f : Rn -> R. Suppose that grad(f(x)) = 0 for all x in some open ball B(a, r). Show that f is constant on B(a, r). [Hint: use part (a) to make this a problem about a function of one variable] part (a) is show that for any two points x, y in B there is a straight line starting at x and ending at y that is contained in B, which I got, but I don't understand what it has to do with anything. Isn't this just a property of the gradient? Any help would be greatly appreciated.