In this paper, we examine sets of tools associated to modeling systems for mathematical programming which can be used to automatically detect the presence or lack of convexity and concavity in the objective and constraint functions. The COCONUT solver system (Schichl, 2004) focuses on nonlinear global continuous optimization and possesses its own modeling language and data structures. The Dr.AMPL (Fourer and Orban, 2007) meta-solver aims to analyze nonlinear diffentiable optimization models and hooks into the AMPL Solver Library (Gay, 2002). We report numerical results using these tools on sets of test problems for both global and local optimization.