7 Fig. 7 shows the curve defined implicitly by the equation
$$y ^ { 2 } + y = x ^ { 3 } + 2 x ,$$
together with the line \(x = 2\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3efea8db-9fa1-47a8-89b8-e4888f87a313-3_465_378_534_808}
\captionsetup{labelformat=empty}
\caption{Not to scale}
\end{figure}
Fig. 7
Find the coordinates of the points of intersection of the line and the curve.
Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\). Hence find the gradient of the curve at each of these two points.