  In the framework of the van-der-Waals model, analytical expressions for the
locus of extrema (ridges) for heat capacity, thermal expansion coefficient,
compressibility, density fluctuation, and sound velocity in the supercritical
region have been obtained. It was found that the ridges for different
thermodynamic values virtually merge into single Widom line only at $T<1.07
T_c, P<1.25P_c$ and become smeared at $T<2T_c, P<5P_c$, where $T_c$ and $P_c$
are the critical temperature and pressure. The behavior of the Batschinski
lines and the pseudo-Gruneisen parameter $\gamma$ of a van-der-Waals fluid were
analyzed. In the critical point, the van-der-Waals fluid has $\gamma=8/3$,
corresponding to a soft sphere particle system with exponent $n=14$.
