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If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula?

  1. 8
  2. 8(1/3)
  3. 8(2/3)
  4. 9
in Numerical Methods by Boss (16.3k points) | 313 views

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Answer: B

f(3) = [(3-2)(3-4)*2]/[(1-2)(1-4)] + [(3-1)(3-4)*4]/[(2-1)(2-4)] + [(3-1)(3-2)*16]/[(4-1)(4-2)]

= -2/3 + 8/2 + 16/3

= 26/3 = 8(1/3).

Ref: https://mat.iitm.ac.in/home/sryedida/public_html/caimna/interpolation/lagrange.html
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