4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b85872d4-00b2-499b-9765-f7559d3de66a-05_716_725_219_603}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = x ^ { 2 } + \frac { 16 } { x } , \quad x > 0$$
The curve has a minimum turning point at \(A\).
- Find \(\mathrm { f } ^ { \prime } ( x )\).
- Hence find the coordinates of \(A\).
- Use your answer to part (b) to write down the turning point of the curve with equation
- \(y = \mathrm { f } ( x + 1 )\),
- \(y = \frac { 1 } { 2 } \mathrm { f } ( x )\).