Edexcel P1 2019 October — Question 7

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2019
SessionOctober
TopicDifferentiation Applications
TypeFind derivative of polynomial

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50ec901b-b6b6-4b72-85bd-a084f313c99b-16_648_822_296_561} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows part of the curve with equation \(y = 2 x ^ { 2 } + 5\) The point \(P ( 2,13 )\) 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, in terms of \(h\), the gradient of the line \(P Q\). Give your answer in simplest form.
  3. Explain briefly the relationship between the answer to (b) and the answer to (a).