  We describe a scheme for finding quantum critical points based on studies of
a non-equilibrium susceptibility during finite-rate quenches taking the system
from one phase to another. We assume that two such quenches are performed in
opposite directions, and argue that they lead to formation of peaks of a
non-equilibrium susceptibility on opposite sides of a critical point. Its
position is then narrowed to the interval marked off by these values of the
parameter driving the transition, at which the peaks are observed. Universal
scaling with the quench time of precision of such an estimation is derived and
verified in two exactly solvable models. Experimental relevance of these
results is expected.
