Let the polynomial $x^4$ be approximated by a polynomial of degree $\leq 2$ which interpolates it at $x=-1,0,1$. Find the maximum absolute interpolation error in the interval [-1,1]
Attempt: Error $\leq (x-x_0)(x-x_1) \cdots (x-x_n) \frac {f^{n+1}(c)}{(n+1)!}$ for some c in the interval.
Now, $f^4=4!$ and the maximum value of $x(x+1)(x-1)$ is $0.38$ for $x=\frac{-1}{\sqrt{3}}$ so my answer is $0.38$. however, the answer is given as the range (-0.1,0.1). Please help!