OK I apologise for the bum-steer.QUID is correct.Best L/D is the holding speed.I do beleive however it is the speed ,the only speed,to give one the lowest burn on the fuel flow guage.That is the name of the game here.And one does attain it by bringing up hold information on the FMC.
"specific range" and "optimum range" I think we are talking about the same thing.Although I believe the latter to be a clearer term.The thing to know here though is how to get it out of that box and I believe one gets it by entering 0 in the cost index field.
As for your next question re E/O speed in the -57 I believe that is best climb gradient speed.After all what is the objective in this scenario....well there is prob. several poss. objectives....but one of the more likely ones is that you are terrain critical,you will therefore want to descend with as shallow angle or path as is poss.
QUID also offers another important consideration in relation to any of the lower type speeds and that is they to tend to be a little unstable