  Synchrotron X-rays can be a useful tool to investigate electron acceleration
at young supernova remnants (SNRs). At present, since the magnetic field
configuration around the shocks of SNRs is uncertain, it is not clear whether
electron acceleration is limited by SNR age, synchrotron cooling, or even
escape from the acceleration region. We study whether the acceleration
mechanism can be constrained by the cutoff shape of the electron spectrum
around the maximum energy. We derive analytical formulae of the cutoff shape in
each case where the maximum electron energy is determined by SNR age,
synchrotron cooling and escape from the shock. They are related to the energy
dependence of the electron diffusion coefficient. Next, we discuss whether
information on the cutoff shape can be provided by observations in the near
future which will simply give the photon indices and the flux ratios in the
soft and hard X-ray bands. We find that if the power-law index of the electron
spectrum is independently determined by other observations, then we can
constrain the cutoff shape by comparing theoretical predictions of the photon
indices and/or the flux ratios with observed data which will be measured by
NuSTAR and/or ASTRO-H. Such study is helpful in understanding the acceleration
mechanism. In particular, it will supply another independent constraint on the
magnetic field strength around the shocks of SNRs.
