The relationship between RPM and power is Power = Torque X RPM.
Since the impedance of the magnetizing branch of the equivalent circuit increases as the frequency increases, it is necessary to maintain the ratio of voltage to frequency relatively constant over the operating range in order to have the optimum magnetic field in the stator.
In some situations, the frequency is increased without increasing voltage at the upper end of the speed range. The resulting reduction in torque capability results in a constant power capability up to some speed at which the power capability decreases.
You have missed quite a bit. You need to study the induction motor equivalent circuit and the related performance equations and curves. Answers to the following questions may be helpful:
When load increases in rotor of induction motor how does stator draws more current?
Torque-Speed Equation for Induction Motor
Why does the V/Hz ratio of a motor affect the magnetic field strength?
Inductor Machines: why is constant flux achieved before reaching nominal speed?