On the bounds for the curvature and higher derivatives of the Isgur-Wise function

We discuss constraints imposed on the zero-recoil curvature and higher derivatives of the Isgur-Wise function by a general quark model. These constraints are expressed as bounds for a given slope parameter, and compared with those based upon analyticity properties of QCD spectral functions. Our results also indicate that in the analysis of the experimental data for semileptonic $B\rar D^{(*)}$ decays it may be important to include at least the third term in the form factor expansion about the zero recoil point.