## Functions and Analysis   ## The Signum Function of the Second Derivative and Its Application to the Determination of Relative Extremes of Fractional Functions (SF2D).

Authors: Jesús Álvarez Lobo

Usually, the complexity of a fractional function increases significantly in its second derivative, so the calculation of the second derivative can be tedious and difficult to simplify and evaluate its value at a point, especially if the abscise isn't an integer. However, to determine whether a point at which cancels the first derivative of a function is a relative extremum (maximum or minimum) of it, is not necessary to know the value of the second derivative at the point but only its sign. Motivated by these facts, we define a signum function for the second derivative of fractional functions in the domain of the roots of the first derivative of the function. The method can dramatically simplify the search for maximum and minimum points in fractional functions and can be implemented by means of a simple algorithm.