We report the analysis of simultaneous multiwavelength data of the high-energy-peaked blazar RGB J0710 + 591 from the Large Area X-ray Proportional Counters, Soft X-ray focusing Telescope, and Ultraviolet Imaging Telescope (UVIT) instruments onboard 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 β_p ∼ 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 β_p ∼ 2.2 or p_2 ∼ 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, γ_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 γ_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.