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Calculate the speed (in km/h) for which the airplane will have the maximum endurance (that is, will remain in the air the longest time).

Since the plane is in steady flight, the thrust of the engines equals the drag force from the air. The power of the engines is thus

[itex]P = F_{air} v[/itex].

I assume that the power is directly proportional to the fuel flow rate, which is inversely proportional to the endurance. Letting the derivative wrt v equal zero gives

[itex]\frac{\mathrm{d}P}{\mathrm{d}v} = 0[/itex]

[itex]v = \sqrt[4]{\frac{\beta}{3\alpha}}[/itex].

Which is not correct. What am I doing wrong?

Thanks

James