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the minimum value

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3. Let I be an interval in R and assume f : I ? R is twice differentiable at all points of I. Suppose that a ? I, f?(a) = 0 and f?(x) ?0 for all x ? I, x ? a. Prove: If f??(a) > 0, then f(c) is the minimum value of f in I; that is f(c) ? f(x) for all x ? I.

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