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\includegraphics[max width=\textwidth, alt={}, center]{0f58de6c-aba7-4a79-a962-c23be3ee0aa9-5_650_1038_260_550} The diagram shows part of the curve \(y = \frac { 1 } { 16 } ( 3 x - 1 ) ^ { 2 }\), which touches the \(x\)-axis at the point \(P\). The point \(Q ( 3,4 )\) lies on the curve and the tangent to the curve at \(Q\) crosses the \(x\)-axis at \(R\).

1. State the \(x\)-coordinate of \(P\). Showing all necessary working, find by calculation
2. the \(x\)-coordinate of \(R\),
3. the area of the shaded region \(P Q R\).