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1. The formula used to compute an approximation for the second derivative of a function f at a point x₀ is

Solution: (d)

The finite difference approximation for the 2^nd derivative of f(x) at x₀ is

( Standard result )

2. Following are the values of a function y(x) : y(–1) = 5, y(1) = 8, dy/dx at x = 0 as per Newton’s central difference scheme is:

(a) 0                                                      (b) 1.5

(c) 2.0                                                  (d) 3.0

[GATE-1999]

Solution: (b)

Given :

y(–1) = 5

y(1) = 8

3. The value of a function f(x) are tabulaed below

Using Newton’s forward difference formula, the cubic polynomial that can be fitted to the above data, is

(a) 2x³ + 7x² – 6x + 2

(b) 2x³ – 7x² + 6x – 2

(c) x³ – 7x² – 6x + 1

(d) 2x³ – 7x² + 6x + 1                                                                                                                          [GATE-2004]

Solution: (d)

The difference table for the given data

x₀ = 0

Newton’s forward difference formula

Note : In examination, the students are advised to check options by putting values of x.