10 Fig. 10 shows the curve with equation \(y = x ^ { 2 } + \frac { 16 } { x }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c55a5f04-3573-4f36-a12c-3755bdd4a45b-5_522_1019_403_394}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Hence calculate the coordinates of the stationary point on the curve.
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) and explain why this confirms that he stationary point is a minimum.
- Using the trapezium rule with 4 intervals, estimate the area between the curve and the \(x\) axis between \(x = 2\) and \(x = 4\).
- State, giving a reason, whether this estimate of the area under-estimates or over-estimates the true area beneath the curve.