11
\includegraphics[max width=\textwidth, alt={}, center]{2d5f452d-f820-40fc-9e22-9d3ac4f0698b-18_661_698_260_717}
The diagram shows part of the curve \(y = 3 \sqrt { } ( 4 x + 1 ) - 2 x\). The curve crosses the \(y\)-axis at \(A\) and the stationary point on the curve is \(M\).
- Obtain expressions for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\int y \mathrm {~d} x\).
- Find the coordinates of \(M\).
- Find, showing all necessary working, 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.