8 A solid rectangular block has a base which measures \(2 x \mathrm {~cm}\) by \(x \mathrm {~cm}\). The height of the block is \(y \mathrm {~cm}\) and the volume of the block is \(72 \mathrm {~cm} ^ { 3 }\).
- Express \(y\) in terms of \(x\) and show that the total surface area, \(A \mathrm {~cm} ^ { 2 }\), of the block is given by
$$A = 4 x ^ { 2 } + \frac { 216 } { x }$$
Given that \(x\) can vary,
- find the value of \(x\) for which \(A\) has a stationary value,
- find this stationary value and determine whether it is a maximum or a minimum.