2026 DSS P1 Q8

A company manufactures open-top rectangular plastic storage boxes, each with a square base of side \(x\) cm and height of \(h\) cm.

Each storage box has an external surface area of 432 cm\(^2\).

1. Show that the volume of the storage box is \(\dfrac{432x-x^3}{4}\) cm\(^3\).[3]
2. Given that \(x\) can vary, find the value of \(x\) for which the volume is stationary and determine its nature.[4]