as the blackbox function has no local minimum or maximum in the search interval, then is't always increasing or decreasing.
as a consequence, this function can be reversed.
i've already made such a <b><i>Removed by Freelancer.com Admin for breaching our Terms and Conditions</i></b> in Delphi. the resolution method uses a dichotomical search, so the number of calls of the blackbox function is minimal. it is Log2(range/interval)
so for a 0.00000001 interval and 0-1 range, it would make 27 calls.
i can translate my delphi function to a dotnet static class, but if you really need maximum performance, you should consider making the whole project as unmanaged code in C language.
i can also make a win32 DLL that you would call from your VB code.