point of inflection and point of horizontal inflection (1 Viewer)

[sanshi]

hi
a few days till the maths exam and im still really stuck on his point
* what the difference between a point of inflection and a point of horizontal inflection? i called up the advice line but the guy just confused me more when he started talking in terms of the cubic curve. any help on this question will be grealtly appreciated

 

[Riviet]

A point of inflection is simply a point on a curve where the concavity changes sign, ie from concave up to concave down OR concave down to concave up. A horizontal POI is a POI but the point where the concavity changes has a gradient of zero when a tangent is drawn through it (horizontal tangent).

 

[the pospinator]

a horizontal point of inflection is basically a turning point and an inflection point put together

say that x=1 is a horizontal point of inflection

this means that:
f ' (1) = 0
f '' (1) = 0

 

[ronaldinho]

is this right

point of inflexion
f"(x) = 0

horizontal pt of inflexion:

f'x = 0
f"(x) = 0

 

[SoulSearcher]

Yes, basically.

 

[soul_VL]

Doesnt all point of infelctions = f'(x)= 0 at some stage, not just horizontal?

 

[Riviet]

Doesnt all point of infelctions = f'(x)= 0 at some stage, not just horizontal?

It can but not always is one.

 

[markus123456789]

I'm not sure if this is too late. But also for a horizontal pt of inflection, the sign of the derivative needs to be tested on either side of the turning pt to determine if its +, 0, + or - ,0, -. because when both f'(x) and f''(x) = 0 it doesnt mean that it has to be a horizontal pt of inflection... i think , someone please correct me if im wrong . Just a thought.. moments before the exam