... solve for one variable in terms of the other(s).6In the process of establishing the above analogy, we first establish the concepts of the firstand second derivatives of an integral (13) about a ... end-point values of y0(x)orη(x)). Form thefamily of arcsy0(x)+η(x) x1≤ x ≤ x2(16)x1[x2]y0Figure 9: Families of arcs y0+ ηThen for sufficiently small values of say −δ ≤ ... The third part of the problem, the determination of an arc satisfying thesufficient conditions, is frequently the most difficult of all, and is the part for which fewestmethods of a general character...