6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0e7cab3d-c1e6-4420-93b4-eca5af704432-06_758_1227_280_443}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
Figure 3 shows a sketch of part of the curve with equation
$$y = x e ^ { - 2 x }$$
The point \(P ( a , b )\) is the turning point of the curve.
- Find the value of \(a\) and the exact value of \(b\)
The finite region \(R\), shown shaded in Figure 3, is bounded by the curve, the line with equation \(y = b\) and the \(y\)-axis.
- Find the exact area of \(R\).