10.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{fc9cd828-f9bc-4cad-8a70-4214697b1c6a-11_707_855_255_539}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\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,
\begin{enumerate}[label=(\alph*)]
\item find the range of values of $x$ for which $\mathrm { f } ( x )$ is increasing,
\item 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 $\int _ { 2 } ^ { 6 } \left( \frac { 36 } { x ^ { 2 } } + 2 x - 13 \right) \mathrm { d } x = - 8$
\item \begin{enumerate}[label=(\roman*)]
\item state the value of $\int _ { 6 } ^ { 9 } \left( \frac { 36 } { x ^ { 2 } } + 2 x - 13 \right) \mathrm { d } x$
\item find the value of the constant $k$ such that $\int _ { 2 } ^ { 6 } \left( \frac { 36 } { x ^ { 2 } } + 2 x + k \right) \mathrm { d } x = 0$
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{Edexcel P2 2019 Q10 [11]}}