12.
\includegraphics[max width=\textwidth, alt={}, center]{e0c7b6f3-9c28-48bd-a401-635efb2521e3-26_504_856_239_657} The figure above shows the curve \(C\) with equation $$f ( x ) = \frac { x + 4 } { \sqrt { x } } , x > 0 .$$ a) Determine the coordinates of the minimum point of \(C\), labelled as \(M\). The point \(N\) lies on the \(x\) axis so that \(M N\) is parallel to the \(y\) axis. The finite region \(R\) is bounded by \(C\), the \(x\) axis, the straight line segment \(M N\) and the straight line with equation \(x = 1\).
b) Use the trapezium rule with 4 strips of equal width to estimate the area of \(R\).
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