vertical and horizontal points of inflection (1 Viewer)

[aanthnnyyy]

Sorry if tis is a stupid question, but just to clarify, is a vertical inflection present when y"=0 and subbing stationary points into y" to find values are different (2 ways of finding infl.)? Because from my knowledge horizontal is when they both exist as the same point.

 

[Joshmosh2]

When y''= 0, you're essentially finding any points of inflexion. I'm not sure where you got the 'vertical' from.
Horizontal points of inflexion occur when there is also a stat. pt. at that particular point. That is because the tangent at that point is horizontal.