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)?

Answer: A. 5 — 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 =…

A.
5
B.
6.5
C.
4
D.
3

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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.

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