6 Differentiate \(10 x ^ { 4 } + 12\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{936dd0c9-0776-47c5-9eb8-613752bbf286-2_507_494_217_839}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
Fig. 10 shows a solid cuboid with square base of side \(x \mathrm {~cm}\) and height \(h \mathrm {~cm}\). Its volume is \(120 \mathrm {~cm} ^ { 3 }\).
- Find \(h\) in terms of \(x\). Hence show that the surface area, \(A \mathrm {~cm} ^ { 2 }\), of the cuboid is given by \(A = 2 x ^ { 2 } + \frac { 480 } { x }\).
- Find \(\frac { \mathrm { d } A } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } A } { \mathrm {~d} x ^ { 2 } }\).
- Hence find the value of \(x\) which gives the minimum surface area. Find also the value of the surface area in this case.