  We consider $C^2$ diffeomorphisms of a closed interval with only parabolic
fixed points. We show that the maximal growth of the derivatives of the
iterates of such a diffeomorphism is exactly quadratic provided it has a non
quadratically tangency to the identity at a fixed point that is topologically
repelling on one side. Moreover, in absence of such fixed points, the maximal
growth of the derivatives of the iterates is subquadratic.
