1. The problem statement, all variables and given/known data Suppose that f has a continuous second derivative for all x, and that f(0) = 1, f'(0) = 2, and f''(0) = 0. Does f have an inflection point at x = 0? 2. Relevant equations none 3. The attempt at a solution I know that for f'' to have a point of inflection, it needs to change sign near that point, but I can't remember if there's a test for f'' that involves f' to find out if it does. Should I just say that it is impossible to say, since I can't analyze the 'neighborhood' of x = 0 to see if f'' changes sign?