8 A cuboid has a volume of \(8 \mathrm {~m} ^ { 3 }\). The base of the cuboid is square with sides of length \(x\) metres. The surface area of the cuboid is \(A \mathrm {~m} ^ { 2 }\).
- Show that \(A = 2 x ^ { 2 } + \frac { 32 } { x }\).
- Find \(\frac { \mathrm { d } A } { \mathrm {~d} x }\).
- Find the value of \(x\) which gives the smallest surface area of the cuboid, justifying your answer.