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MAX RANGE & MAX ENDURANCE

MAX RANGE = GO AS FAR AS YOU CAN (MAXIMIZE NMI/LB OF FUEL)

MAX ENDURANCE = STAY UP AS LONG AS YOU CAN (MAXIMIZE HR/LB OF FUEL)

Both are related to the "power curve" of fuel flow ( = thrust (power)) vs airspeed 

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for a given altitude, there is one airspeed which results in the minimum fuel flow
(∴ flying along at this speed burns gas at lowest rate, gas lasts longer)