Optimize for integers

Dec 2015
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Optimize for integers the function: \(\displaystyle f(x)=\dfrac{px}{x-p} \; \), p-parameter.
 

skipjack

Forum Staff
Dec 2006
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2,332
Does "optimize" mean "minimize the time needed to calculate" or something else?
 
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skipjack

Forum Staff
Dec 2006
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2,332
For $x \in \mathbb{Z}$, $f(x)$ is maximized when $x = \lfloor p \rfloor + 1$, and minimized when $x = \lceil p \rceil - 1$.
 
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skipjack

Forum Staff
Dec 2006
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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.
 
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