5 The diagram shows an open-topped water tank with a horizontal rectangular base and four vertical faces. The base has width \(x\) metres and length \(2 x\) metres, and the height of the tank is \(h\) metres.
\includegraphics[max width=\textwidth, alt={}, center]{33da89e2-f74f-4d5a-8bbd-ceaa728b6c34-4_403_410_477_792} The combined internal surface area of the base and four vertical faces is \(54 \mathrm {~m} ^ { 2 }\).

1. 1. Show that \(x ^ { 2 } + 3 x h = 27\).
   2. Hence express \(h\) in terms of \(x\).
   3. Hence show that the volume of water, \(V \mathrm {~m} ^ { 3 }\), that the tank can hold when full is given by $$V = 18 x - \frac { 2 x ^ { 3 } } { 3 }$$
2. 1. Find \(\frac { \mathrm { d } V } { \mathrm {~d} x }\).
   2. Verify that \(V\) has a stationary value when \(x = 3\).
3. Find \(\frac { \mathrm { d } ^ { 2 } V } { \mathrm {~d} x ^ { 2 } }\) and hence determine whether \(V\) has a maximum value or a minimum value when \(x = 3\).
   (2 marks)