10 Fig. 10 shows a sketch of the curve \(y = x ^ { 2 } - 4 x + 3\). The point A on the curve has \(x\)-coordinate 4 . At point B the curve crosses the \(x\)-axis.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{19552108-0808-4946-a937-9074d58519b2-4_768_734_500_667}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
- Use calculus to find the equation of the normal to the curve at A and show that this normal intersects the \(x\)-axis at \(\mathrm { C } ( 16,0 )\).
- Find the area of the region ABC bounded by the curve, the normal at A and the \(x\)-axis.