3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0d458344-42cb-48d1-90b3-e071df8ea7bb-08_693_987_116_482}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C _ { 1 }\) with equation
$$y = \frac { 4 x } { 4 - | x | }$$
and the curve \(C _ { 2 }\) with equation
$$y = x ^ { 2 } - 8 x$$
For \(x > 0 , C _ { 1 }\) has equation \(y = \frac { 4 x } { 4 - x }\)
- Use algebra to show that \(C _ { 1 }\) touches \(C _ { 2 }\) at a point \(P\), stating the coordinates of \(P\)
- Hence or otherwise, using algebra, solve the inequality
$$x ^ { 2 } - 8 x > \frac { 4 x } { 4 - | x | }$$