SPS SPS FM 2020 June — Question 6

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2020
SessionJune
TopicProduct & Quotient Rules

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.
  1. 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.
  2. Find the exact area of \(R\).