Here is the question:
With the knowledge that $f$ has derivative in point $a$ and $k>h>0$, show that this limit does not necessarily exist: \begin{align*} lim_{k,h \rightarrow 0^+} \frac{f(a+k) - f(a+h)}{k-h} \end{align*}
Up until this point I tried functions like $f(x) = e^x$ and polynomial functions. which only made me more suspicious about the correctness of problem. Though my closest try was $f(x) = \sqrt{x}$ at point $0$ which almost works but fails to be differentiable at point $0$. I have also tried to approach $k,h$ in a special way for example the substitution $h = k^n$ for sufficiently large $n$ makes things a little easier but at the end I failed to find a definite answer.
Now I dont know if the claim is true or not (it may not be and the limit may always exist) but if so, a nice counter would be very appreciated.
Thanks.