  The decrease of both the rolling speed of the inflaton and the sound speed of
the curvature perturbations can amplify the curvature perturbations during
inflation so as to generate a sizable amount of primordial black holes. In the
ultraslow-roll inflation scenario, it has been found that the power spectrum of
curvature perturbations has a $k^4$ growth. In this paper, we find that when
the speed of sound decreases suddenly, the curvature perturbations becomes
scale dependent in the infrared limit and the power spectrum of the curvature
perturbation only has a $k^2$ growth. Furthermore, by studying the evolution of
the power spectrum in the inflation model, in which both the sound speed of the
curvature perturbations and the rolling speed of the inflaton are reduced, we
find that the power spectrum is nearly scale invariant at the large scales to
satisfy the constraint from the cosmic microwave background radiation
observations, and at the same time can be enhanced at the small scales to
result in an abundant formation of primordial black holes. In the cases of the
simultaneous changes of the sound speed and the slow-roll parameter $\eta$ and
the change of the sound speed preceding that of the slow-roll parameter $\eta$,
the power spectrum can possess a $k^6$ growth under certain conditions, which
is the steepest growth of the power spectrum reported so far.
