2014 TWO(d)

The hourly cost of running an aeroplane depends on the speed at which it flies.

For a particular aeroplane this is given by the equation

$C=4v+\frac{1000000}{v},200\le v\le 800$

where $C$ is the hourly cost of running the aeroplane, in dollars per hour
and $v$ is the airspeed of the aeroplane, in kilometres per hour.

Find the minimum hourly cost at which this aeroplane can be flown.

*Show any derivatives that you need to find when solving this problem.*