Best methods of interpolation for certain classes of differentiable functions

For the class $W^{(r)}L_q(M;a,b)$, $1\le q\le\infty$, we construct the best method of approximation of the functional $f(x)$, $x\in[a,b]$, among all the methods using only information about the values of $f^{(k)}(k=0,1,\dots,r-1;i=1,2,\dots,N)$.