Question: Let f be continuous on an open interval I containing c and be differentiable at any x in I with x ~= c. Suppose that

Let f be continuous on an open interval I containing c and be differentiable at any x in I with x ~= c. Suppose that the limit limxc f'(x) exists. Prove that f is differential at c and f '(c)= limxc f '(x).

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