 Solution

The explicit divided difference formula makes $M_i(t)$ a finite linear combination of $(t_j-t{)}_{+}^{k-1}$. It is therefore polynomial of degree at most $k-1$ between knots and globally $C^{k-2}$. For $t<t_i$, the nodal data come from a polynomial of degree $k-1$, whose order-$k$ divided difference vanishes; for $t\ge t_{i+k}$ all truncated powers vanish. Thusand normalization does not change the degree, smoothness, knots, or support.