( optional). Let f be continuous on [a, b] and differentiable in (a, 6). Show that if lim f'6) = A, then f'la) exists and equals A. Hint: Use the definition of f'la) and the mean value Theorem. )

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A: Given query is to find f(x).

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A: Please see the below picture for detailed solution.

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A: This question is based on Rolle's theorem which is explained in step 2.

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