Mean Value Theorem for Several Variables If f is differentiable at each point of the line segment from a to b, then there exists on that line segment a point c between a and b such that
((b) - ((a) = (((c) ( (b - a)
Assuming that this result is true, show that, if f is differentiable on a convex set S and if (((p) = 0 on S, then f is constant on S. A set S is convex if each pair of points in S can be connected by a line segment in S.