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I have a short package like this:

BeginPackage["FunctionAnalysis`",{"Global`"}];
MonoIntervals::usage="returns monotonic intervals of given function";
Begin["`Private`"];
FunctionAnalysis`Private`MonoIntervals[func_[arg_],var_]:={Reduce[D[func[arg],var]>0,var]}
End[];
EndPackage[];

I include it, and when I call, for example:

MonoIntervals[Sin[x],x]

it executes MonoIntervals. The problems occurs when I try to call MonoIntervals with functions like:

f[x_]:=x^2+2*x-10
MonoIntervals[f[x],x]

this results in 

Out[25]=MonoIntervals[-10 + 2 x + x^2, x]

Why doesn't the function execute?

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Because MonoIntervals[f[x],x] will evaluate like this:

  1. MonoIntervals[f[x], x]
  2. MonoIntervals[x^2+2*x-10, x]

And it stops there because x^2+2*x-10 doesn't match the pattern func_[arg_]. What precisely are you trying to achieve by using this pattern?

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  • $\begingroup$ I am trying to get intervals where given function is positive. What pattern would suit for my case? I thought I have to use func_[arg_], if I replace it with MonoIntervals[func_,arg_] and use later in Reduce[D[func,arg]>0,arg] it still doesn't evaluate. $\endgroup$ – Kristians Kuhta Dec 19 '14 at 16:47
  • $\begingroup$ @KristiansKuhta Have you seen the tutorial on patterns? If you are still unsure about why your function behaves the way it does, it's a good idea to stop for a moment and read through it. $\endgroup$ – Szabolcs Dec 19 '14 at 17:01

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