- Fig. 6 shows the region enclosed by part of the curve \(y = 2 x ^ { 2 }\), the straight line \(x + y = 3\), and the \(y\)-axis. The curve and the straight line meet at \(\mathrm { P } ( 1,2 )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f4c02a9b-802e-4e51-94c2-d1c5d69855b5-04_552_806_287_625}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
The shaded region is rotated through \(360 ^ { \circ }\) about the \(y\)-axis. Find, in terms of \(\pi\), the volume of the solid of revolution formed.
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\section*{2. a)}
Find, in terms of \(k\), the set of values of \(x\) for which
$$k - | 2 x - 3 k | > x - k$$
giving your answer in set notation.
b)
Find, in terms of \(k\), the coordinates of the minimum point of the graph with equation
$$y = 3 - 5 \mathrm { f } \left( \frac { 1 } { 2 } x \right)$$
where
$$\mathrm { f } ( x ) = k - | 2 x - 3 k |$$
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