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Part BCSIR NET December 2025check-the-fourth-difference-before-assuming-all-five-points-force-a-degree-four-fit

Check the fourth difference before assuming all five points force a degree four fit

If p(x) is the interpolating polynomial for the data x = −2,−1,0,1,2 with y = −1,3,1,−1,3, then the value of p(1/2) is

  1. A.−3/8✓
  2. B.−5/8
  3. C.5/8
  4. D.3/8

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Related counterexample: Increasing the number of equally spaced interpolation nodes improves the approximation

More on this topic

The chapter behind this: Interpolation and numerical integration — free to read

From Numerical Analysis › Interpolation and numerical integration with error terms

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