10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fc9cd828-f9bc-4cad-8a70-4214697b1c6a-11_707_855_255_539}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve \(C\) with equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = \frac { 36 } { x ^ { 2 } } + 2 x - 13 \quad x > 0$$
Using calculus,
- find the range of values of \(x\) for which \(\mathrm { f } ( x )\) is increasing,
- show that \(\int _ { 2 } ^ { 9 } \left( \frac { 36 } { x ^ { 2 } } + 2 x - 13 \right) \mathrm { d } x = 0\)
The point \(P ( 2,0 )\) and the point \(Q ( 6,0 )\) lie on \(C\).
Given \(\int _ { 2 } ^ { 6 } \left( \frac { 36 } { x ^ { 2 } } + 2 x - 13 \right) \mathrm { d } x = - 8\) - state the value of \(\int _ { 6 } ^ { 9 } \left( \frac { 36 } { x ^ { 2 } } + 2 x - 13 \right) \mathrm { d } x\)
- find the value of the constant \(k\) such that \(\int _ { 2 } ^ { 6 } \left( \frac { 36 } { x ^ { 2 } } + 2 x + k \right) \mathrm { d } x = 0\)