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Part CCSIR NET December 2024the-correction-vanishes-at-the-old-nodes

The correction vanishes at the old nodes

Let f(x) be the polynomial of degree at most 2 that interpolates the data (−1, 2), (0, 1), and (1, 2). If g(x) is a polynomial of degree at most 3 such that f(x) + g(x) interpolates the data (−1, 2), (0, 1), (1, 2), and (2, 17), then

  1. A.f(5) + g(3) = 50
  2. B.2f(5) − g(3) = 4✓
  3. C.f(1) + g(3) = 50✓
  4. D.f(5) + g(3) = 74✓

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.

See pricing

50 are analysed free — try those first.

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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