OCR MEI C2 — Question 5

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
TopicDifferentiation from First Principles

5 In Fig. 5, A and B are the points on the curve \(y = 2 ^ { x }\) with \(x\)-coordinates 3 and 3.1 respectively. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e15637e4-8532-4b8b-9c95-7a4359503c7b-2_703_728_1199_754} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure}
  1. Find the gradient of the chord AB . Give your answer correct to 2 decimal places.
  2. Stating the points you use, find the gradient of another chord which will give a closer approximation to the gradient of the tangent to \(y = 2 ^ { x }\) at A .