3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c08fbab-283e-4c92-89a4-10f68f37e133-05_799_885_118_534}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\), where
$$\mathrm { f } ( x ) = ( 2 x - 5 ) \mathrm { e } ^ { x } , \quad x \in \mathbb { R }$$
The curve has a minimum turning point at \(A\).
- Use calculus to find the exact coordinates of \(A\).
Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has exactly two roots,
- state the range of possible values of \(k\).
- Sketch the curve with equation \(y = | \mathrm { f } ( x ) |\).
Indicate clearly on your sketch the coordinates of the points at which the curve crosses or meets the axes.