Differentiation - Problems Involving Maximisation and Minimisation

The diagram shows a square planting field \(PQRS\) of side \(4\) km. \(T\) and \(U\) are on sides \(PQ\) and \(PS\), respectively, such that \(QT = US = x\) km.

1. Show that the area, \(A\) km\(^2\), of quadrilateral \(TRSU\), is given by
   \(A = -\frac{1}{2}x^2 + 2x + 8.\)
2. Given that \(x\) can vary, find the value of \(x\) for which \(A\) has a stationary value.
3. Explain why this value of \(x\) maximises the value of \(A\).