10 A curve for which \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = 2 x - 5\) has a stationary point at \(( 3,6 )\).
- Find the equation of the curve.
- Find the \(x\)-coordinate of the other stationary point on the curve.
- Determine the nature of each of the stationary points.
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The diagram shows part of the curve \(y = \frac { 3 } { \sqrt { ( 1 + 4 x ) } }\) and a point \(P ( 2,1 )\) lying on the curve. The normal to the curve at \(P\) intersects the \(x\)-axis at \(Q\). - Show that the \(x\)-coordinate of \(Q\) is \(\frac { 16 } { 9 }\).
- Find, showing all necessary working, the area of the shaded region.
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