10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2ce10759-9ce6-47a1-b55d-d22082f88f55-26_707_992_246_539}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the curve \(C\) with parametric equations
$$x = ( t + 3 ) ^ { 2 } \quad y = 1 - t ^ { 3 } \quad - 2 \leqslant t \leqslant 1$$
The point \(P\) with coordinates \(( 4,2 )\) lies on \(C\).
- Using parametric differentiation, show that the tangent to \(C\) at \(P\) has equation
$$3 x + 4 y = 20$$
The curve \(C\) is used to model the profile of a slide at a water park.
Units are in metres, with \(y\) being the height of the slide above water level. - Find, according to the model, the greatest height of the slide above water level.