3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6f577461-24b7-4615-b58b-e67597fd9675-08_815_849_248_607}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C\), shown in Figure 1, has equation
$$y ^ { 2 } x + 3 y = 4 x ^ { 2 } + k \quad y > 0$$
where \(k\) is a constant.
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\)
The point \(P ( p , 2 )\), where \(p\) is a constant, lies on \(C\).
Given that \(P\) is the minimum turning point on \(C\), - find
- the value of \(p\)
- the value of \(k\)