Is a point of inflection concave or convex? - Which answer is correct?

[Sarah66]

Homework Statement

Hello everybody, :)
I have a problem with determining the intervals of convexity and concavity of this function:

Relevant Equations

there are no inflection points here for me

but for me there is no solution to this inequality...
I never wait for a ready answer but I've already spent 4 hours on it and I still don't know what to mark...

 

[haruspex]

there are no inflection points here for me

There doesn’t need to be an inflection point to switch between concave and convex if there are points where the function is undefined.

 

[BiGyElLoWhAt]

Check the sign of the 2nd derivative on each interval if you aren't sure.