- A diesel lorry is driven from Birmingham to Bury at a steady speed of v kilometres per hour. The total cost of the journey, \(\pounds C\), is given by
$$C = \frac { 1400 } { v } + \frac { 2 v } { 7 } .$$
- Find the value of \(v\) for which \(C\) is a minimum.
- Find \(\frac { \mathrm { d } ^ { 2 } C } { \mathrm {~d} v ^ { 2 } }\) and hence verify that \(C\) is a minimum for this value of \(v\).
- Calculate the minimum total cost of the journey.