Package function not evaluating

Question

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?

Answer 1

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?