What exactly is an inflection point?

(An example of the types of questions you could ask here)

If you have an equation such as f(x)=x^4 , the double derivative will be f^(2)(x) = 12x^2 .

This double derivative will equal zero at x = 0 , but f(x) will not change concavity.

An inflection point is defined as a point where the curve changes concavity in the book, but then it is defined as that before double derivatives are brought into the picture; I think it's possible that an inflection point might be defined as simply a point where f''=0 . But then it might not be.

I will try to ask this in class tomorrow, but if I don't, feel free to post your opinion as a comment.