After this question : [Does every real function have this weak continuity property?](https://mathoverflow.net/questions/309019/does-every-real-function-have-this-weak-continuity-property) 


Natrualy there are an other (more difficult) :



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> Is it true that for every real function $f:\mathbb{R}\to\mathbb{R}$, there exists a real sequence $(x\_n)\_n$, taking values different from $c$, converging to some real number $c$, such that the sequence $\left(\dfrac{f(c)-f(x\_n)}{c-x\_n}\right)\_n$ converges ?
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> 
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Does every real function have this weak derivation property?
the answer is yes : <http://webhome.auburn.edu/~brownj4/tatras.pdf>


PS : the answer was in the comments, but no one gave an answer


