Given $f(x)=\cos(\pi x)$
a) Calculate the interpolation polynomial such that $p(-1)=f(-1)$, $p'(-1)=f'(-1)$, $p(0)=f(0)$, $p(1)=f(1)$ and $p'(1)=f'(1)$.
b) Show that $|f(x)-p(x)|\leq\frac{\pi^5}{120}$ for every $x\in[-1,1]$
So I managed to do item a) and obtain $p(x)=2x^4-4x^2+1$. However, when I try to do item b) and bound my error, I have repeated nodes, $x_0=-1$ and $x_2=1$ and therefore im not sure if I can use the bound I would like to use, say:
$$||W_{n+1}(x)||_{\infty}\leq\left(\frac{b-a}{2}\right)^{n+1}$$
Since my nodes are equidistant. Is there an aditional condition I should add because of the repetition of my nodes?