9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f39ade34-32e2-4b5c-b80a-9663c6a65c87-14_609_744_223_593}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = \frac { 8 } { x } + \frac { 1 } { 2 } x - 5 , \quad 0 < x \leqslant 12$$
The curve crosses the \(x\)-axis at \(( 2,0 )\) and \(( 8,0 )\) and has a minimum point at \(A\).
- Use calculus to find the coordinates of point \(A\).
- State
- the roots of the equation \(2 \mathrm { f } ( x ) = 0\)
- the coordinates of the turning point on the curve \(y = \mathrm { f } ( x ) + 2\)
- the roots of the equation \(\mathrm { f } ( 4 x ) = 0\)