Getting error of interpolating polynomial by subtraction.

Question

$f(x)= \frac{1}{1+x^2}$

and when I computed the interpolating polynomial of 5 equally spaced points in [-5,5] I got

$ p(x)= 0.0053x^4 -0.1711x^2 +1$

Now I need to estimate the error in the interpolant using the error formula.

$|f(x)-p(x)|=\left|\frac{f^{(5)}(\xi)}{(5)!}\prod_{i=0}^4(x-x_i)\right|$

I'm trying to self learn this topic and I want to know if there is a way I can use f(x)-p(x) to solve this instead of using the right side of the formula.

Answer 1

I think the problem asks you to do it from the right hand side. You need to find the fifth derivative of $f(x)$ then according to the property of that function, find its maximum value to estimate the largest error.