Using the Lagrange method to find the polynomial that interpolates the points:

f(x) | -3 | -2 | -1 | 0 | 1 |

x | -197 | -35 | -1 | 1 | 5 |

I find:

$\displaystyle p(x) = y_0 L_0(x) + y_1 L_1(x) + y_2 L_2(x) + y_3 L_3(x) + y_4 L_4(x)$

$\displaystyle L_0(x) = \frac{x^4 + 30x^3 - 176x^2 -30x -175}{1269952992}$

$\displaystyle L_1(x) = \frac{x^4 + 192x^3 -986x^2 -192x + 985}{-7931520}$

$\displaystyle L_2(x) = \frac{x^4 +228x^3 -402x^2 -4750x + 4925}{779968}$

$\displaystyle L_3(x) = \frac{x^4 +228x^3 + 52x^2 -5100x -4925}{-57024}$

$\displaystyle L_4(x) = \frac{x^4 +232x^3 +984x^2 -232x -985}{193920}$

So I got the following polynomial:

$\displaystyle p(x) = 4.124x10^{-4}x^4 + 9,55x10^{-4}x^3 +5,34x10^{-3}x^2 +4,845x10^{-3}x + 0,0111$

Is this correct what I did?