Approximation of poly of degree 4 by degree 2

Question

Let $(x)=x^4$ be approximated by a polynomial of degree less or equal to 2, which interpolates $x^4$ at x = -1,0,1then the maximum absolute interpolation error over the interval[-1,1] is equal to?

Answer 1

You have three points on $f(x)=x^4$. Find a quadratic $g(x)$ that passes throught these three points. Then you are looking for $\max |f(x)-g(x)|$. Compute it as a function of $x$, take the derivative, set to zero ...