I idontknow Dec 2015 859 115 Earth Friday at 11:18 PM #1 Optimize for integers the function: \(\displaystyle f(x)=\dfrac{px}{x-p} \; \), p-parameter.

skipjack Forum Staff Dec 2006 21,184 2,332 Saturday at 2:57 AM #2 Does "optimize" mean "minimize the time needed to calculate" or something else? Reactions: idontknow

I idontknow Dec 2015 859 115 Earth Saturday at 5:26 AM #3 Find Maximal and minimal value of the function for integers.

skipjack Forum Staff Dec 2006 21,184 2,332 Saturday at 6:40 AM #4 For $x \in \mathbb{Z}$, $f(x)$ is maximized when $x = \lfloor p \rfloor + 1$, and minimized when $x = \lceil p \rceil - 1$. Reactions: idontknow

For $x \in \mathbb{Z}$, $f(x)$ is maximized when $x = \lfloor p \rfloor + 1$, and minimized when $x = \lceil p \rceil - 1$.

skipjack Forum Staff Dec 2006 21,184 2,332 Sunday at 2:03 AM #6 I inspected the graph of the function for various values of $p$. I didn't allow for $p = 0$, so that case needs to be considered separately. Last edited: Sunday at 2:10 AM Reactions: idontknow

I inspected the graph of the function for various values of $p$. I didn't allow for $p = 0$, so that case needs to be considered separately.