11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{423eb549-0873-4185-8faf-12dedafcd108-17_600_1024_221_470}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve \(C\) with equation
$$y = \mathrm { e } ^ { a - 3 x } - 3 \mathrm { e } ^ { - x } , \quad x \in \mathbb { R }$$
where \(a\) is a constant and \(a > \ln 4\)
The curve \(C\) has a turning point \(P\) and crosses the \(x\)-axis at the point \(Q\) as shown in Figure 2.
- Find, in terms of \(a\), the coordinates of the point \(P\).
- Find, in terms of \(a\), the \(x\) coordinate of the point \(Q\).
- Sketch the curve with equation
$$y = \left| \mathrm { e } ^ { a - 3 x } - 3 \mathrm { e } ^ { - x } \right| , \quad x \in \mathbb { R } , \quad a > \ln 4$$
Show on your sketch the exact coordinates, in terms of \(a\), of the points at which the curve meets or cuts the coordinate axes.