11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{129adfbb-98fa-4e88-b636-7b4d111f3349-28_647_855_244_605}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of part of the curve \(C _ { 1 }\) with equation
$$y = 2 x ^ { 3 } + 10 \quad x > 0$$
and part of the curve \(C _ { 2 }\) with equation
$$y = 42 x - 15 x ^ { 2 } - 7 \quad x > 0$$
- Verify that the curves intersect at \(x = \frac { 1 } { 2 }\)
The curves intersect again at the point \(P\)
- Using algebra and showing all stages of working, find the exact \(x\) coordinate of \(P\)