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\includegraphics[max width=\textwidth, alt={}, center]{fdd6e942-b5bc-4369-8587-6de120459776-18_557_677_264_733}
The diagram shows a curve with equation \(y = 4 x ^ { \frac { 1 } { 2 } } - 2 x\) for \(x \geqslant 0\), and a straight line with equation \(y = 3 - x\). The curve crosses the \(x\)-axis at \(A ( 4,0 )\) and crosses the straight line at \(B\) and \(C\).
- Find, by calculation, the \(x\)-coordinates of \(B\) and \(C\).
- Show that \(B\) is a stationary point on the curve.
- Find the area of the shaded region.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.