8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a9870c94-0910-46ec-a54a-44a431cb324e-22_524_1443_260_246}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve \(y = \mathrm { f } ( x )\), where
$$\mathrm { f } ( x ) = \frac { 6 x + 2 } { 3 x ^ { 2 } + 5 } , \quad x \in \mathbb { R }$$
- Find \(\mathrm { f } ^ { \prime } ( x )\), writing your answer as a single fraction in its simplest form.
The curve has two turning points, a maximum at point \(A\) and a minimum at point \(B\), as shown in Figure 2.
- Using part (a), find the coordinates of point \(A\) and the coordinates of point \(B\).
- State the coordinates of the maximum turning point of the function with equation
$$y = \mathrm { f } ( 2 x ) + 4 \quad x \in \mathbb { R }$$
- Find the range of the function
$$\operatorname { g } ( x ) = \frac { 6 x + 2 } { 3 x ^ { 2 } + 5 } , \quad x \leqslant 0$$