Let f : Rn -> R.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Gradient and open ball

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