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I have the following two functions of $x$:

$ f(x) = \frac{c}{c + (N-1)o + Nd + xl}$

$g(x) = ae + (1-a)\frac{1}{x+2N}$

with $0 \leq a, e, c, o, d, l \leq 1$ and $N, x \in \mathbb{N}^+$.

For both functions increasing $x$ is obviously associated with a decreasing value of the function. And both decreases are non-linear (as $x$ is in the denominator).

Is there a way to further differentiate the functions with respect to how strong they decrease or any other information of how they differentially react to changes in $x$?

Henrik
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  • That's a subjective question, but I would argue "not really", since both functions are O(1/x). –  Oct 26 '14 at 16:32
  • @barrycarter I am actually interested in relatively small values of $x$, say $x < 100$. So O() is perhaps not the most relevant. – Henrik Oct 26 '14 at 16:42

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