A ship is sailing with speed \(v\text{ km h}^{-1}\).
The sailing cost per hour, \(\$C\), is given by \(C=v^2+\dfrac{3000}{v}+100\).
Find the speed that makes \(C\) a minimum.
Justify that this value of \(C\) is a minimum.[5]
Hence find the minimum sailing cost for a journey of 150 km.[3]
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Answer:(a) \(11.4\text{ km h}^{-1}\) (b) \(\$6460\) using the speed from (a), as in the official mark scheme. The unrestricted minimum journey cost is \(\$4875\); see the wording note.