9
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{faeaf2aa-ed4e-4926-b402-40c4c9aad479-3_535_790_450_630}
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\caption{Fig. 9}
\end{figure}
Fig. 9 shows a sketch of the graph of \(y = x ^ { 3 } - 10 x ^ { 2 } + 12 x + 72\).
- Write down \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Find the equation of the tangent to the curve at the point on the curve where \(x = 2\).
- Show that the curve crosses the \(x\)-axis at \(x = - 2\). Show also that the curve touches the \(x\)-axis at \(x = 6\).
- Find the area of the finite region bounded by the curve and the \(x\)-axis, shown shaded in Fig. 9 . [4]