5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08756c4b-6619-42da-ac8a-2bf065c01de8-14_787_638_251_653}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with parametric equations
$$x = 5 + 2 \tan t \quad y = 8 \sec ^ { 2 } t \quad - \frac { \pi } { 3 } \leqslant t \leqslant \frac { \pi } { 4 }$$
- Use parametric differentiation to find the gradient of \(C\) at \(x = 3\)
The curve \(C\) has equation \(y = \mathrm { f } ( x )\), where f is a quadratic function.
- Find \(\mathrm { f } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a\), \(b\) and \(c\) are constants to be found.
- Find the range of f.