8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{23689deb-7eed-4022-848f-1278231a4056-20_915_924_303_580}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 3 shows a sketch of the curve \(C\) with equation
$$y = x ^ { 3 } - 14 x + 23$$
The line \(l\) is the tangent to \(C\) at the point \(A\), also shown in Figure 3.
Given that \(l\) has equation \(y = - 2 x + 7\)
- show, using calculus, that the \(x\) coordinate of \(A\) is 2
The line \(l\) cuts \(C\) again at the point \(B\).
- Verify that the \(x\) coordinate of \(B\) is - 4
The finite region, \(R\), shown shaded in Figure 3, is bounded by \(C\) and \(l\).
Using algebraic integration, - show that the area of \(R\) is 108