12 Fig. 12 is a sketch of the curve \(y = 2 x ^ { 2 } - 11 x + 12\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b4c0b4b0-f13c-49a9-9f98-f86f28d1f577-5_478_951_333_792}
\captionsetup{labelformat=empty}
\caption{Fig. 12}
\end{figure}
- Show that the curve intersects the \(x\)-axis at \(( 4,0 )\) and find the coordinates of the other point of intersection of the curve and the \(x\)-axis.
- Find the equation of the normal to the curve at the point \(( 4,0 )\).
Show also that the area of the triangle bounded by this normal and the axes is 1.6 units \(^ { 2 }\).
- Find the area of the region bounded by the curve and the \(x\)-axis.