hello im having trouble with understanding the point of inflection, in my math text book using the first derivative i found out that the stationary point both have a gradient less than zero on both of its side which is a point of inflection property, however some people say that to find the point of inflection you use the 2nd derivative and see how concavity changes, this is the point i get confused on... you can see the whole problem in the pictures below...

can you identify a point of inflection using the first derivative?

please explain it step by step because im very confused on this part...

thank you in advance