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Eco-Driving is a critical technology for improving automotive transportation efficiency. It is achieved by modifying the driving trajectory over a particular route to minimize required propulsion energy. Eco-Driving can be approached as an optimal control problem subject to driving constraints such as traffic lights and positions of other vehicles. In this paper we demonstrate the connection between Eco-Driving and best interpolation in the strip which is a problem in approximation theory and optimal control. By exploiting this connection, we are able to generate optimal Eco-Driving trajectories that can be driven with an autonomous system and evaluate them using conventional, hybrid electric, and fully electric vehicle models from FASTSim software. Our results quantify the energy efficiency improvements that can be achieved with the proposed approach.