6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{44035bf8-f54c-472a-b969-b4fa4fa3d203-18_579_643_255_653}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
\section*{In this question you must show all stages of your working.}
Solutions relying entirely on calculator technology are not acceptable.
The function f is defined by
$$f ( x ) = 5 \left( x ^ { 2 } - 2 \right) ( 4 x + 9 ) ^ { \frac { 1 } { 2 } } \quad x \geqslant - \frac { 9 } { 4 }$$
- Show that
$$f ^ { \prime } ( x ) = \frac { k \left( 5 x ^ { 2 } + 9 x - 2 \right) } { ( 4 x + 9 ) ^ { \frac { 1 } { 2 } } }$$
where \(k\) is an integer to be found.
- Hence, find the values of \(x\) for which \(\mathrm { f } ^ { \prime } ( x ) = 0\)
Figure 3 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\).
The curve has a local maximum at the point \(P\)
- Find the exact coordinates of \(P\)
The function g is defined by
$$g ( x ) = 2 f ( x ) + 4 \quad - \frac { 9 } { 4 } \leqslant x \leqslant 0$$
- Find the range of g