How to determine full-load RPM of an induction motor at any arbitrary frequency?
It may be irrelevant. Many VFDs use slip compensation.


  Slip Compensation
  Slip compensation is actually a sophisticated version of
  the open loop concept. The slip compensation method
  of speed control does not monitor the actual shaft RPM.
  Rather, it utilizes drive output current transducers to
  monitor the current drawn by the connected motor.
  As discussed earlier, when a load is placed on a NEMA
  B design motor during a situation where the output
  frequency is held constant, the slip increases, the shaft
  RPM slows and the motor current increases. The
  difference here is that the “slip” function “compensates”
  for the reduction in shaft RPM by increasing the voltage
  and frequency applied to the motor. 
  Figure 2 illustrates
  an application that requires the motor to supply full
  torque at 1500 RPM.





  The top portion shows what occurs without slip
  compensation. The applied frequency is 50Hz, but the
  motor actual shaft RPM, due to slip, has a value of
  1455. The bottom portion shows how slip compensation
  automatically "compensates" this situation by applying
  1.5Hz additional output frequency to the existing output
  frequency of 50Hz, resulting in a new output frequency
  of 51.5Hz. The motor shaft still "slips" back, but now the
  actual shaft speed is the desired 1500 RPM.
  The amount of slip does not actually decrease. It is
  simply shifted so that the actual RPM now is the desired
  RPM. Remember that the drive monitors current drawn
  by the motor, not the actual shaft RPM.


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