If f(1) = 4 and f(5) = 6, then using Lagrange interpolation, what is the value…
2021
If f(1) = 4 and f(5) = 6, then using Lagrange interpolation, what is the value of f(3)?
- A.
5
- B.
6.5
- C.
4
- D.
3
Attempted by 5 students.
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Correct answer: A
Using the two-point Lagrange interpolation formula for (1, 4) and (5, 6):
f(3) = 4 * (3 - 5)/(1 - 5) + 6 * (3 - 1)/(5 - 1)
= 4 * (1/2) + 6 * (1/2)
= 2 + 3
= 5.
Therefore, f(3) = 5.