4.01: Minimum sailing cost

0606/22/F/M/26 — Question 7 · 8 marks

A ship is sailing with speed \(v\text{ km h}^{-1}\). The sailing cost per hour, \(C\) dollars, is given by \(C=v^2+\dfrac{3000}{v}+100\).
(a)
Find the speed that makes \(C\) a minimum. Justify that this value of \(C\) is a minimum.
[5]
(b)
Hence find the minimum sailing cost for a journey of \(150\) km.
[3]