Edexcel AS Paper 1 2021 November — Question 5

Exam BoardEdexcel
ModuleAS Paper 1 (AS Paper 1)
Year2021
SessionNovember
TopicDifferentiation Applications
TypeFind tangent line equation

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{235cd1dc-a3ab-473a-bf77-3e41b274dfd8-10_680_684_255_694} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows part of the curve with equation \(y = 3 x ^ { 2 } - 2\)
The point \(P ( 2,10 )\) lies on the curve.
  1. Find the gradient of the tangent to the curve at \(P\). The point \(Q\) with \(x\) coordinate \(2 + h\) also lies on the curve.
  2. Find the gradient of the line \(P Q\), giving your answer in terms of \(h\) in simplest form.
  3. Explain briefly the relationship between part (b) and the answer to part (a).