10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1528bec3-7a7a-42c5-bac2-756ff3493818-18_508_812_306_644}
\captionsetup{labelformat=empty}
\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 \(k\).