Question: Suppose that r > 0, that a Rn, and that f: Br(a) Rm. If all first-order partial derivatives of f exist on Br(a)

Suppose that r > 0, that a ∈ Rn, and that f: Br(a) → Rm. If all first-order partial derivatives of f exist on Br(a) and satisfy fxj(x) = 0 for all x ∈ Br(a) and all j = 1, 2,..., n, prove that f has only one value on

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