points of inflexion/horizontal inflexion (1 Viewer)

[blacktown_]

I'm so confused with inflection and horizontal inflection
are they the same thing?
what is the best way to see if there is a horizontal inflection. by using the first derivative,with the test of turning points
or the second derivative, with the test for concavity?

 

[Trebla]

A point of inflexion is a point where there is a change in concavity on either side of the point. A horizontal point of inflexion is a special type of point of inflexion where the point also has a horizontal slope on the curve.

 

[Carrotsticks]

Algebraically, a normal point of inflexion just satisfies y''=0 whereas a horizontal point of inflexion satisfies that AND y'=0.

 

[blacktown_]

ok cool thanks !