Given f(20) = 512, f(30) = 439, f(40) = 346, f(50) = 243. Consider the following statements: 1. The function f(x) can be approximated by a polynomial of degree n where n < 2. 2. The approximate value of f(x) for x=10 and x=60 can be obtained by Newton Gregory forward difference and Newton Gregory backward difference formulae respectively. Which of the above statements is/are correct?

Q74Section I (Objective (Q1–Q80))74 of 80

Numerical Analysis — detecting the required polynomial degree and choosing extrapolation formulas

Given $f(20) = 512$ , $f(30) = 439$ , $f(40) = 346$ , $f(50) = 243$ .

Consider the following statements:

The function $f(x)$ can be approximated by a polynomial of degree $n$ where $n < 2$ .
The approximate value of $f(x)$ for $x=10$ and $x=60$ can be obtained by Newton Gregory forward difference and Newton Gregory backward difference formulae respectively.

Which of the above statements is/are correct?

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