y = z dt/dx
The formulas of transformation are thus:
x = a(t + κt2 + λt3),
Maximum and Minimum Points. Since only curves with one maximum point or mode are practically useful it is desirable to determine what values of the constants a, κ and λ give unimodal curves.
We have
From the vanishing of the numerator of dy/dx there must result either one or three real modes for each pair of values for λ and κ, that is, for each translated curve. To determine what values of λ and κ give uni-modal curves and what tri-modal it is convenient to consider the plane of λ and κ.