A generalized four-vertex theorem

Analytic Non-Borel Sets and Vertices of Differentiable Curves in the Plane

“…Moreover, the subject of vertex theorems occupied the mind of several generations of mathematicians starting with the proof in 1909 of the original Four Vertex Theorem, concerning local extrema of the curvature, by the Indian mathematician S. Mukhopadhaya (see [20]). The MathSciNet contains several items concerning vertex theorems from which, according to their reviews, we selectively refer the reader to [1], [2], [4], [5], [7], [8], [9], [10], [13], [14], [15], [16], [23], [26], [28], [29], [32], and [33].…”