Thanks Sean again for the detailed explanation.
Unfortunately, this is only a 'simpler' example to illustrate what originally i was struggling. My real problems deals with bigger models with lots of other parameters, not just two.
Note that in the most recent reply, ?NumericQ was note used. That was part of the reason why I did not use it in the first instance. Apart from the likelihood estimates, I was also trying to use D[] to work out hessian (2nd derivative), and ect.
mylik[f0_?NumericQ, p_?NumericQ] := -Log[2] - Log[120] -
Log[6227020800] - Log[1124000727777607680000] -
Log[15511210043330985984000000] + f0 Log[(1 - p)^6] +
25 Log[6 (1 - p)^5 p] + 22 Log[15 (1 - p)^4 p^2] +
13 Log[20 (1 - p)^3 p^3] + 5 Log[15 (1 - p)^2 p^4] +
Log[6 (1 - p) p^5] + 2 Log[p^6] - LogGamma[1 + f0] +
LogGamma[69 + f0]
FullSimplify[D[mylik[f0, p], p] == 0]
(will not work with ?NumericQ )
In order to build up a larger function (programm), i did not use ?NumericQ.
But again, your input is really helpful to me as I have only been using MMA substantially for just about 3 weeks.
For now,
FindRoot[proflikfun[f0], {f0, 0, 10}]
FindRoot[proflikfun[f0], {f0, 10, 20}]
works fine. I will try to get around with more lines, and hopefully generalize it for my other data sets and models.