Question 2 - A-Level Maths

Exam Board	OCR MEI
Module	Further Numerical Methods (Further Numerical Methods)
Year	2021
Session	November
Topic	Sign Change & Interval Methods
Type	Polynomial Interpolation from Data

2 The table shows some values of \(x\) and the associated values of \(\mathrm { f } ( x )\).

\(x\)	1	2	3	4	5
\(\mathrm { f } ( x )\)	- 0.65	- 0.35	1.77	5.71	11.47

Complete the difference table in the Printed Answer Booklet.
Explain why the data may be interpolated by a polynomial of degree 2.
Use Newton's forward difference interpolation formula to obtain a polynomial of degree 2 for the data.