10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{089c3b5b-22ab-4fa2-8383-4f30cefa792a-14_515_833_251_552}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = x ^ { 2 } ( 9 - 2 x )$$
There is a minimum at the origin, a maximum at the point \(( 3,27 )\) and \(C\) cuts the \(x\)-axis at the point \(A\).
- Write down the coordinates of the point \(A\).
- On separate diagrams sketch the curve with equation
- \(y = \mathrm { f } ( x + 3 )\)
- \(y = \mathrm { f } ( 3 x )\)
On each sketch you should indicate clearly the coordinates of the maximum point and any points where the curves cross or meet the coordinate axes.
The curve with equation \(y = \mathrm { f } ( x ) + k\), where \(k\) is a constant, has a maximum point at \(( 3,10 )\).
- Write down the value of \(k\).