11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{96e004d9-c6b6-474b-9b67-06e1771c609e-22_760_1182_248_443}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\).
The curve \(C\) crosses the \(x\)-axis at the origin, \(O\), and at the points \(A\) and \(B\) as shown in Figure 5.
Given that
$$f ^ { \prime } ( x ) = k - 4 x - 3 x ^ { 2 }$$
where \(k\) is constant,
- show that \(C\) has a point of inflection at \(x = - \frac { 2 } { 3 }\)
Given also that the distance \(A B = 4 \sqrt { 2 }\)
- find, showing your working, the integer value of \(k\).