After this question : Does every real function have this weak continuity property?

Natrualy there are an other (more difficult) :

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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