In the present document, the exact solution to the mean value theorem problem applied to the maximum power point (MPP) calculation is presented, and an improvement to this solution is developed based on an expression of the MPP that depends on the optimal load and the characteristic parameters of the photovoltaic (PV) module. The validation of the approximations is performed by comparing with the numerical solution of the 5-parameter single diode model of 11 commercial modules with different technologies, as well as by comparison with existing approximations in the literature.