# 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 $I_{N}$

## Question ID - 157052 | Toppr Answer 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 $I_{N}$

$I_{L}$ and $I_{N}$ are always equal