  We consider multimodal C^3 interval maps f satisfying a summability condition
on the derivatives D_n along the critical orbits which implies the existence of
an absolutely continuous f -invariant probability measure mu. If f is
non-renormalizable, mu is mixing and we show that the speed of mixing (decay of
correlations) is strongly related to the rate of growth of the sequence D_n as
n tends to infinity . We also give sufficient conditions for mu to satisfy the
Central Limit Theorem. This applies for example to the quadratic Fibonacci map
which is shown to have subexponential decay of correlations.
