Derived functors of graded algebras

A number of spectral sequences arising in homotopy theory have the derived functors of a graded algebraic functor as their E²-term. We here describe conditions for the vanishing of such derived functors, yielding vanishing lines for the spectral sequences. We also show that under these conditions the nth derived functor, for large n, depends only on low-dimensional information. The applications we have in mind include certain cases of the Bousfield-Kan spectral sequence, the Quillen homology of a graded algebra (with applications to H. Miller's Grothendieck spectral sequence), and the wedge, smash, and homology spectral sequences.