7. Suppose that V is open in Rn , f: V -+ R is C2 on V,

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7. Suppose that V is open in Rn , f: V -+ R is C2 on V, and fxJa) = ° for some a E V and all j = 1, ... , n. Prove that if H is a compact convex subset of V, then there is a constant M such that for all x E H If(x) - f

(a) I :::; Mllx-aI12 .

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