8 A solid rectangular block has a square base of side \(x \mathrm {~cm}\). The height of the block is \(h \mathrm {~cm}\) and the total surface area of the block is \(96 \mathrm {~cm} ^ { 2 }\).
- Express \(h\) in terms of \(x\) and show that the volume, \(V \mathrm {~cm} ^ { 3 }\), of the block is given by
$$V = 24 x - \frac { 1 } { 2 } x ^ { 3 }$$
Given that \(x\) can vary,
- find the stationary value of \(V\),
- determine whether this stationary value is a maximum or a minimum.