The commonly used exchange-correlation functionals of density functional theory and their potentials are examined numerically following the first such investigation by Perdew. They are also investigated for Ne and Kr. Their behaviour for large gradients of the density and for large distances is not satisfactory. In particular, the correct asymptoticr-1behaviour is difficult to achieve. Following van Leeuwen and Baerends, this is linked to the energy ϵmaxof the highest occupied orbital arising from the Kohn-Sham equations. This deficiency is linked also with the poor prediction of molecular polarizabilities.