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High Quality Content by WIKIPEDIA articles! In mathematics, Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. It gives a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function derivative is zero in that point). So, by using Fermat's theorem, the potential extremums of a function displaystyle f, with derivative displaystyle f', are found by solving an equation in displaystyle f'. Fermat's theorem gives only a necessary condition for extreme function values, and some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can determine if any stationary point is a maximum, minimum, or inflection point.