Where k - number of points in each segment.
Extrema of such measure are determined by zero values of its derivative:
The denominator of resulting expression is positive at any values of entering variables. The numerator can be transformed to the view
This equation has five solutions, one of which is x_1 = 0, and four others :
Two solutions which are determined by a difference of the expressions placed under sign of exterior square root, have imaginary values at any values of entering variables (as x_0> 0, under the initial agreement - see fig.5a). Others two have real values, when
Simplifying this expression, we shall obtain that at D < sqrt(3)*x_0 investigated conformity function has three extremums: one central and two symmetric side ones. It is easy to show, that:
It is obvious, if D < sqrt(3)*x_0, then S"(x)|_0 > 0, i.e. the central extremum is a local minimum of considered conformity function of and, hence, adjacent side exremums are local maximums of this function (see fig.5b). At D > sqrt(3)*x_0, these maximums merge in one (see fig.5c). Positions of maximums depending on a value of parameter D are shown on fig.5d (see the formula for an evaluation of x_2... x_5).