26A48; 26D10.

Assuming that a ``derivative'' ratio of the ratio of differentiable functions and is strictly monotonic (that is, is increasing or decreasing), it was shown in previous papers that then can switch at most once, from decrease to increase or vice versa. In the present paper, it is shown that, if is non-strictly monotonic (that is, non-increasing or non-decreasing), then can have at most one maximal interval of constancy (m.i.c.); on the other hand, any one m.i.c. of a given derivative ratio is the m.i.c. of an appropriately constructed original ratio .;