maxsmooth fits derivative constrained functions (DCF) such as Maximally Smooth Functions (MSFs) to data sets. MSFs are functions for which there are no zero crossings in derivatives of order m >= 2 within the domain of interest. They are designed to prevent the loss of signals when fitting out dominant smooth foregrounds or large magnitude signals that mask signals of interest. Here "smooth" means that the foregrounds follow power law structures and do not feature turning points in the band of interest. maxsmooth uses quadratic programming implemented with CVXOPT (ascl:2008.017) to fit data subject to a fixed linear constraint, Ga <= 0, where the product Ga is a matrix of derivatives. The code tests the <= 0 constraint multiplied by a positive or negative sign and can test every available sign combination but by default, it implements a sign navigating algorithm.