- #1
eridanus
- 10
- 0
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.
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.