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

Q. 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 IL, and then by the Newton polynomial, denoted by IN. Which one of the following statements is correct?

(A) IL is always greater than IN

(B) IL and IN are always equal

(C) IL is always less than IN

(D) No definite relation exists between IL and IN

Ans: No definite relation exists between IL and IN