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I want to find third degree Lagrange polynomial for these four points:$(1,2),(2,9),(3,28),(4,65)$.

I know how to use formula to find that. but I want to know whether this alternative method is ok or not:

Suppose we have $y=f(x)$:

$$f(1)=1^3+1$$ $$f(2)=2^3+1$$ $$f(3)=3^3+1$$ $$f(4)=4^3+1$$

Therefore $f(x)=x^3+1$ passes through these four points. Can I consider this function as Lagrange polynomial if problem explicitly mention use Lagrange Interpolation?

Etemon
  • 6,437

1 Answers1

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Absolutely, as the Lagrangian polynomial is unique. You don't have to justify how you obtained the coefficients (provided the degree of the polynomial you exhibit does not exceed the number of points minus one).