We report the analysis of simultaneous multi-wavelength data of the high energy peaked blazar RGB J0710+591 from the LAXPC, SXT and UVIT instruments on-board AstroSat. The wide band X-ray spectrum (0.35 -- 30 keV) is modelled as synchrotron emission from a non-thermal distribution of high energy electrons. The spectrum is unusually curved, with a curvature parameter $beta_p sim 6.4$ for a log parabola particle distribution, or a high energy spectral index $p_2 > 4.5$ for a broken power-law distribution. The spectrum shows more curvature than an earlier quasi-simultaneous analysis of Swift-XRT/NuSTAR data where the parameters were $beta_p sim 2.2$ or $p_2 sim 4$. It has long been known that a power-law electron distribution can be produced from a region where particles are accelerated under Fermi process and the radiative losses in acceleration site decide the maximum attainable Lorentz factor, $gamma_{max}$. Consequently, this quantity decides the energy at which the spectrum curves steeply. We show that such a distribution provides a more natural explanation for the AstroSat data as well as the earlier XRT/NuSTAR observation, making this as the first well constrained determination of the photon energy corresponding to $gamma_{max}$. This in turn provides an estimate of the acceleration time-scale as a function of magnetic field and Doppler factor. The UVIT observations are consistent with earlier optical/UV measurements and reconfirm that they plausibly correspond to a different radiative component than the one responsible for the X-ray emission.
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