From Boeing Jet Transport Performance Methods, Chapter 33: Cruise - Engine Failure and Driftdown (rev. March 2009)
Failure of One Engine in Cruise
At the point of engine failure, the pilots will set thrust on the remaining engine(s) to the Maximum Continuous Thrust rating. You will remember that MCT is a special thrust rating usable only in case of emergency.
What speed should they maintain during the descent? It makes sense to use a descent speed that will minimize the descent gradient, thus keeping the descent flight path as high as possible.
In the chapter entitled “Climb Angle and Rate of Climb” we talked about the effect of speed on an airplane’s climb gradient. There, you saw that the speed for the best possible gradient is approximately the speed at which the ratio of drag to lift is at its minimum value. For planning the descent performance of an airplane following engine(s) failure, we will base our calculations on the use of the speed for the best gradient, which is referred to in the AFM as the “enroute climb speed”. Don’t let the use of the term “climb” in that name confuse you: the climb referred to can be either a positive gradient or a negative one. In either case, the speed is the same.