5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{52f73407-14c5-46e6-b911-aa096b9b5893-08_701_1125_246_443}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with the equation \(y = \left( 2 x ^ { 2 } - 5 x + 2 \right) \mathrm { e } ^ { - x }\).
- Find the coordinates of the point where \(C\) crosses the \(y\)-axis.
- Show that \(C\) crosses the \(x\)-axis at \(x = 2\) and find the \(x\)-coordinate of the other point where \(C\) crosses the \(x\)-axis.
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Hence find the exact coordinates of the turning points of \(C\).