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?

(A) $I_{L}$ is always greater than $I_{N}$

(B) $I_{L}$ and $I_{N}$ are always equal

(C) $I_{L}$ is always less than $I_{N}$

(D) No definite relation exists between $I_{L}$ and $I_{N}$

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?

(A) $I_{L}$ is always greater than $I_{N}$

(B) $I_{L}$ and $I_{N}$ are always equal

(C) $I_{L}$ is always less than $I_{N}$

(D) No definite relation exists between $I_{L}$ and $I_{N}$

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