We propose a parametric Kantorovich theorem, which will achieve these two tasks. The idea is to compute worst case Kantorovich constants with respect to parameters q using a branch and bound algorithm dedicated to nonlinear nonsmooth global optimization. A rigorous first order model of the dependence with respect to parameters p is used to enforce the convergence of the error upper-bound. Details about these developments can be found in [1]. We provide here a different point of view, in particular emphasizing the reason why not using the interval Newton operator, in spite of its theoretical superiority on Kantorovich theorem in this context [2].