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Part CCSIR NET June 2024interpolate-around-the-unknown-value

Interpolate around the unknown value

Let g(x) be the polynomial of degree at most 4 that interpolates the data (x, y) = (−1, −30), (0, 1), (2, c), (3, 10), (6, 19). If g(4) = 5, then which of the following statements are true?

  1. A.c = 13
  2. B.g(5) = 6✓
  3. C.g(1) = 14✓
  4. D.c = 15✓

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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