Solution
= Solution
For $M=\max\{|s|,|t|,1\}$, factorization of a difference of powers gives
$$
|s^j-t^j|
=|s-t|\left|\sum_{l=0}^{j-1}s^{j-1-l}t^l\right|
\leq jM^{j-1}|s-t|.
$$
Consequently the <polynomial> $f$ obeys the <Lipschitz bound>
$$
\boxed{|f(s)-f(t)|\leq A M^{d-1}|s-t|,
\qquad
A=\sum_{j=1}^dj|\alpha_j|.}
$$