7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c320b71-8793-461a-a078-e4f64c144a3a-20_618_841_267_555}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\), where
$$f ( x ) = ( x + 4 ) ( x - 2 ) ( 2 x - 9 )$$
Given that the curve with equation \(y = \mathrm { f } ( x ) - p\) passes through the point with coordinates \(( 0,50 )\)
- find the value of the constant \(p\).
Given that the curve with equation \(y = \mathrm { f } ( x + q )\) passes through the origin,
- write down the possible values of the constant \(q\).
- Find \(\mathrm { f } ^ { \prime } ( x )\).
- Hence find the range of values of \(x\) for which the gradient of the curve with equation \(y = \mathrm { f } ( x )\) is less than - 18
\includegraphics[max width=\textwidth, alt={}, center]{6c320b71-8793-461a-a078-e4f64c144a3a-23_68_37_2617_1914}