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\includegraphics[max width=\textwidth, alt={}, center]{ed5b77ae-6eac-4e73-bc43-613433abd3e1-16_723_942_260_598}
The diagram shows part of the curve \(y = \sqrt { } ( 4 x + 1 ) + \frac { 9 } { \sqrt { } ( 4 x + 1 ) }\) and the minimum point \(M\).
- Find expressions for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\int y \mathrm {~d} x\).
- Find the coordinates of \(M\).
The shaded region is bounded by the curve, the \(y\)-axis and the line through \(M\) parallel to the \(x\)-axis. - 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.