2 Fig. 7 shows the curve defined implicitly by the equation
$$y ^ { 2 } + y = x ^ { 9 } + 2 x$$
together with the line \(x = 2\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e0636807-d5bf-43c2-a484-68245e639cee-2_462_385_657_858}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
Not to scale
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.