Economic and financial mathematics uses elements of mathematical analysis (N-dimensional space, rows, series, derivation, integration), probability calculus and linear algebra (vector, linear system of equations, programming) in all areas of economics. In this paper we analyse the EUR / USD exchange rate between 01/13/2017 - 02/15/2018. The sample element number of the examined data set is 420,544 (four hundred and twenty thousand five hundred and fortyfour). Name of the data: standard critical points (O, H, L, C) of a one-minute time window. Especially what we want to know about EUR / USD exchange rate? We want to know when the trend ends. When we want to know the end of a trend, we look for the inflection point of the function. The condition for the existence of the inflection point is that there exists a third-order derivative of the function and the second-order derivative at this point must be equal to zero, and that the third-order derivative must not be equal to zero. In this research we use histogram, moving average, the 12-day and 26-day averages for the study period, polynomial trend determination, the linear trend definition, the polynomial average of the examined period, the logarithmic trend and special the sixth degree polynomial for analyse and for possibility of forecasting using an econometric model. With the help of the Excel spreadsheet, it was possible to project in a certain number of steps. We made the projection for five step lengths. Forecasting has proved to be a good approach to what has actually happened, which is a good reason for us to continue working and to keep the direction we have started, to do further research in the specific field.