If f(1) = 2,f(2) = 4 and f(4) = 16,what is the value of f(3) using Lagrange’s…
2004
If f(1) = 2,f(2) = 4 and f(4) = 16,what is the value of f(3) using Lagrange’s interpolation formula?
- A.
8
- B.
8 1/3
- C.
8 2/3
- D.
9
Show answer & explanation
Correct answer: C
Use the Lagrange interpolation formula for the points (1,2), (2,4), and (4,16). At x = 3, the basis contributions are: for x=1, 2*((3-2)*(3-4))/((1-2)*(1-4)) = -2/3; for x=2, 4*((3-1)*(3-4))/((2-1)*(2-4)) = 4; for x=4, 16*((3-1)*(3-2))/((4-1)*(4-2)) = 16/3. Hence f(3) = -2/3 + 4 + 16/3 = 26/3 = 8 2/3.