[tzs]

It sounds like you are describing curves that are strictly convex. Curves that are convex, but not strictly convex, can intersect their tangents at more than one point, or even at every point.

I'm going by the definition of convex function given in Rudin's "Principles of Mathematical Analysis", Apostol's "Calculus", Wikipedia, and MathWorld.

[telchar]

Fair enough. I suppose pointing out that the authors merely omitted "strictly" wouldn't have served GP's point as well.

[graycat]

Strictly convex need have no role in this Google ML material. Just convex is enough.