I wanted to ask something regarding the finite difference approximation. I used the finite difference to calculate the numerical derivatives of my function. The finite difference is given by the following formula:

\begin{equation}
\frac{f(x+h)-f(x)}{h}
\end{equation}

The value of $h$ is questionable. In theory we should take it as small as possible, but I am not sure if we can just pick random different values for $h$ and try to see which one works better or if there is any "rule" or constraint to pick up a good value of $h$.

With Thanks