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## Homework Statement

Let I be an interval, and f: I --> R be a continuous function that is known to be differentiable on I except at c. Assume that f ' : I \ {c} --> R admits a continuous continuation to c (lim x -> c f ' exists). Show that f is in fact also differentiable at x and f ' (c) = lim x->c f '.

## The Attempt at a Solution

This seems like a very easy question to me, but for some reason its stumping me, maybe because of the way my prof worded it, but I am just a little confused. I know i need to use the mean value theorem, but I am still stuck. Please help.