The base of a cuboid has sides of length \(x\) cm and \(3x\) cm. The volume of the cuboid is \(288 \text{ cm}^3\).

(i) Show that the total surface area of the cuboid, \(A \text{ cm}^2\), is given by

\(A = 6x^2 + \frac{768}{x}.\)

(ii) Given that \(x\) can vary, find the stationary value of \(A\) and determine its nature.