3. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
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\caption{Figure 1}
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Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = ( x - 2 ) ^ { 2 } \mathrm { e } ^ { 3 x } \quad x \in \mathbb { R }$$
The curve has a maximum turning point at \(A\) and a minimum turning point at \(( 2,0 )\)
- Use calculus to find the exact coordinates of \(A\).
Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has at least two distinct roots,
- state the range of possible values for \(k\).