13
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7791371e-26d9-428c-8700-5121a1c6464a-4_456_387_1539_833}
\captionsetup{labelformat=empty}
\caption{Fig. 13}
\end{figure}
Fig. 13 shows a sketch of the curve \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = x ^ { 3 } - 5 x + 2\).
- Use the fact that \(x = 2\) is a root of \(\mathrm { f } ( x ) = 0\) to find the exact values of the other two roots of \(\mathrm { f } ( x ) = 0\), expressing your answers as simply as possible.
- Show that \(\mathrm { f } ( x - 3 ) = x ^ { 3 } - 9 x ^ { 2 } + 22 x - 10\).
- Write down the roots of \(\mathrm { f } ( x - 3 ) = 0\).