question archive Let f(x) be a differentiable function on (1,3)

Let f(x) be a differentiable function on (1,3)

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Let f(x) be a differentiable function on (1,3). Suppose limx->2f'(x) exists, i.e. the limit of f'(x), as x approaches 2, exists and is finite.

How do I prove that f'(x) is continuous at x=2.

pur-new-sol

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