Let $f$ be a continuous function on the interval $[a,b]$ such as for all x in $(a,b)$ :
The right hand derivative equals $0$.
Is $f$ constant?
The obvious reflex one would have is to try to find a counter-example, I tried, many times and I always failed.
I assumed it to be true and tried to prove it, I tried manipulating sequences, it never worked.
I tried calculating the left hand derivative of a point by using a sequence, it seemed to work at first, but it didn't as well.
All in all, I think $f$ may not be necessarily constant.