If f(x) = x2, then the second order divided difference for the points x0, x1, x2 will be:

This question was previously asked in
AAI (ATC) Junior Executive Official Paper (Held On: 30 Nov 2018 Shift 2)
View all AAI JE ATC Papers >
  1. -1
  2. \(\dfrac{-1}{x_1 - x_0}\)
  3. 1
  4. \(\dfrac{1}{x_2-x_1}\)

Answer (Detailed Solution Below)

Option 3 : 1
Free
AAI ATC JE Physics Mock Test
6.6 K Users
15 Questions 15 Marks 15 Mins

Detailed Solution

Download Solution PDF

Concept:

If data points are given as a function of f, then the various order divided differences are as follows,

Zeroth-order divided difference:

f[x0] = f(x0);

First-order divided difference:

\(f[x_0,x_1] = \frac{{f\left( {{x_1}} \right) - f\left( {{x_0}} \right)}}{{{x_1} - {x_0}}};\)

Second-order divided difference:

\(f[x_0,x_1,x_2] = \frac{{f\left[ {{x_1,x_2}} \right] - f\left[ {{x_0,x_1}} \right]}}{{{x_2} - {x_0}}};\)

\(f[x_0,x_1,x_2] = \frac{{\frac{{f\left( {{x_2}} \right) - f\left( {{x_1}} \right)}}{{{x_2} - {x_1}}} - \frac{{f\left( {{x_1}} \right) - f\left( {{x_0}} \right)}}{{{x_1} - {x_0}}}}}{{{x_2} - {x_0}}};\)

Calculation:

Given f(x) = x2;

Using the second-order divided difference formula, we get 

\(f[x_0,x_1,x_2] = \frac{{\frac{{x_2^2 - x_1^2}}{{{x_2} - {x_1}}} - \frac{{x_1^2 - x_0^2}}{{{x_1} - {x_0}}}}}{{{x_2} - {x_0}}};\)

\(\Rightarrow f[x_0,x_1,x_2] = \frac {(x_2+x_1) - (x_1+x_0)}{x_2 - x_0} = 1\)

∴ the second-order divided difference of x2 is 1.

Latest AAI JE ATC Updates

Last updated on May 26, 2025

-> AAI ATC exam date 2025 will be notified soon. 

-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025. 

-> AAI JE ATC 2025 notification is released on 4th April 2025, along with the details of application dates, eligibility, and selection process.

-> Total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.

-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in Airports Authority of India (AAI).

-> The Selection of the candidates is based on the Computer Based Test, Voice Test and Test for consumption of Psychoactive Substances.

-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).

-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.

-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.

More Numerical Methods Questions

Get Free Access Now
Hot Links: teen patti win teen patti cash teen patti octro 3 patti rummy teen patti all game teen patti 3a