Using the White�s density matrix renormalization group, we study a strongly correlated system of fermions confined in an external potential. This system can be modelled by the one-dimensional Hubbard model with a quadratic confining potential. This model describe 6Li or 40K atoms trapped in an optical lattice, which has been studied experimentally and theoretically since the realization of Bose-Einstein condensation of alkali atoms. The fermion density profiles and their variance were computed. We observe coexistence of insulating and metallic regions in the system, this evidence a quantum critical behavior.