8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bef290fb-fbac-4c9c-981e-5e323ac7182e-22_687_698_255_685}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\), where
$$f ( x ) = ( 2 x + 1 ) ^ { 3 } e ^ { - 4 x }$$
- Show that
$$\mathrm { f } ^ { \prime } ( x ) = A ( 2 x + 1 ) ^ { 2 } ( 1 - 4 x ) \mathrm { e } ^ { - 4 x }$$
where \(A\) is a constant to be found.
- Hence find the exact coordinates of the two stationary points on \(C\).
The function g is defined by
$$g ( x ) = 8 f ( x - 2 )$$
- Find the coordinates of the maximum stationary point on the curve with equation \(y = g ( x )\).