If f(x) changes concavity at x=a then there is a point of inflection at x=a.

If f(x) has a point of inflection at x=a, then the tangent line crosses the graph of the function at this point.

If f(x) has a point of inflection at x=a, then f'(x)=0 at x=a.

If f(x) has a point of inflection at x=a then x=a must be in the domain of f.