10.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{135bc546-9274-4862-b2e7-c11e9c8e2c4f-13_1018_1029_287_445}
\end{figure}
Figure 1 shows part of the curve \(C\) with equation \(y = 2 x + \frac { 8 } { x ^ { 2 } } - 5 , x > 0\).
The points \(P\) and \(Q\) lie on \(C\) and have \(x\)-coordinates 1 and 4 respectively. The region \(R\), shaded in Figure 1, is bounded by \(C\) and the straight line joining \(P\) and \(Q\).
- Find the exact area of \(R\).
- Use calculus to show that \(y\) is increasing for \(x > 2\).