  We report the spectroscopic confirmation of four further white dwarf members
of Praesepe. This brings the total number of confirmed white dwarf members to
eleven making this the second largest collection of these objects in an open
cluster identified to date. This number is consistent with the high mass end of
the initial mass function of Praesepe being Salpeter in form. Furthermore, it
suggests that the bulk of Praesepe white dwarfs did not gain a substantial
recoil kick velocity from possible asymmetries in their loss of mass during the
asymptotic giant branch phase of evolution. By comparing our estimates of the
effective temperatures and the surface gravities of WD0833+194, WD0840+190,
WD0840+205 and WD0843+184 to modern theoretical evolutionary tracks we have
derived their masses to be in the range 0.72-0.76Msun and their cooling ages
\~300Myrs. For an assumed cluster age of 625+/-50Myrs the infered progenitor
masses are between 3.3-3.5Msun. Examining these new data in the context of the
initial mass-final mass relation we find that it can be adequately represented
by a linear function (a0=0.289+/-0.051, a1=0.133+/-0.015) over the initial mass
range 2.7Msun to 6Msun. Assuming an extrapolation of this relation to larger
initial masses is valid and adopting a maximum white dwarf mass of 1.3Msun, our
results support a minimum mass for core-collapse supernovae progenitors in the
range ~6.8-8.6Msun.
