The Minkowski question-mark function \( ?(x) \) is a continuous monotone
function defined on \( [0,1] \) interval. It is well known fact that the
derivative of this function, if exists, can take only two values:
\( 0 \) and \( +\infty \). It is also known that the value of the derivative
\( ?'(x) \) at the point \( x=[0;a_1,a_2,\ldots,a_t,\ldots] \) is connected
with the limit behaviour of the arithmetic mean
\( (a_1+a_2+\cdots+a_t)/t \).

Particularly, N. Moshchevitin and A. Dushistova showed that if

\[
a_1+a_2+\cdots+a_t < \kappa_1 t, \]

where

\[
\kappa_1=
\frac{2\log\!\left(\frac{1+\sqrt{5}}{2}\right)}
{\log 2}
=
1.3884\ldots,
\]

then \( ?'(x)=+\infty \). They also proved that the constant
\( \kappa_1 \) is non-improvable. We consider a dual problem:
how small can be the quantity
\( a_1+a_2+\cdots+a_t-\kappa_1 t \)
if we know that \( ?'(x)=0 \)?
We obtain the non-improvable estimates on this quantity.