- In this question you should show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
\begin{figure}[h]
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\caption{Figure 2}
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Figure 2 shows a sketch of part of the curve \(C\) with equation
$$y = x ^ { 3 } - 10 x ^ { 2 } + 27 x - 23$$
The point \(P ( 5 , - 13 )\) lies on \(C\)
The line \(l\) is the tangent to \(C\) at \(P\)
- Use differentiation to find the equation of \(l\), giving your answer in the form \(y = m x + c\) where \(m\) and \(c\) are integers to be found.
- Hence verify that \(l\) meets \(C\) again on the \(y\)-axis.
The finite region \(R\), shown shaded in Figure 2, is bounded by the curve \(C\) and the line \(l\).
- Use algebraic integration to find the exact area of \(R\).