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 !!
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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