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The value of the function $f(x)$ is given at $n$ distinct values of $x$ and its value is to be interpolated at the point $x^*$, using all the $n$ points. The estimate is obtained first by the Lagrange polynomial, denoted by $I_L$, and then by the Newton polynomial, denoted by $I_N$. Which one of the following statements is correct?

  1. $I_L$ is always greater than $I_N$
  2. $I_L$ and $I_N$ are always equal
  3. $I_L$ is always less than $I_N$
  4. Not definite relation exists between $I_L$ and $I_N$
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