If you're below 5k rpm...you will be slow. Gotta keep those RPMs up there. Was your instructor familiar with BMWs? Specifically M cars?
Maybe the instructor was scared. There's a lot of power when you're high in the RPM band. Doesn't take much unsmoothness (word???) to get the rear end drifting out. IMO, gear selection and throttle smoothness is far more critical in my E90 M3 than my E46. If you get it right you will be very richly rewarded.
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2018 F30 320iX Melbourne Red
2011 E90 M3 Monte Carlo Blue
2004 E46 M3 Imola Red
2000 E36/7 Z3 Steel Blue
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