MHB Are Corners Inflection Points on a Graph?

[karush]

in that at corners are not differentiable, does this mean that they also are not inflection points but at the same time a change in the rate.

https://www.physicsforums.com/attachments/517
on the graph above f(x) for [0,7] at x=4 and x=5 what is f' and f'' or does it not exist

thanks ahead(Dull)

 

[Ackbach]

From what I have read, an inflection point is a point at which the curvature or concavity changes sign. Since curvature is only defined where the second derivative exists, I think you can rule out corners from being inflection points.

Great question, by the way! It reminds me of the question of whether, given a function defined on a closed interval, whether the endpoints are critical points (since the two-sided derivative does not exist there).