1) Did you apply a separating bias to the sample? That's a prerequisite in order to have useful data since you need to differentiate between spectrometer and sample secondaries. Your data looks more like that of an unbiased sample since 3.9-4.0 eV is a typical order of magnitude for a semiconductor workfunction.
2) Regarding the actual cutoff determination: we usually used the middle of the secondary electron edge (thus interpretating lower energies as broadening) as the cutoff value, but in our samples the cutoff was usually sharper than the one shown here so a base point interpretation wouldn't have made a difference for the first decimal.