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Sunday, December 8, 2013

Question of the week #1 - the answer

Question of the week - #1

   ok, so here we have the answer to last week's question on the continuity of the derivative function at a given point ...
   The answer is in general negative! A function may be differentiable at a point of its domain, with the derivative being discontinuous at that point! Here is a counterexample. you can provide a proof on your own by directly applying the definition of the derivative at $x=0$, but if you find the computation cumbersome, here are some more details ;)

Enjoy !!

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