Let me make this very clear. If x is inflection, then the second derivative at x is going to be equal to 0. Because you're having a change in the concavity, I always say con-ca-ti-vity, but it's the con-cavity. You have a change in the slope goes from either increasing to decreasing or from decreasing to increasing. But if the derivative is equal to 0, you cannot assume that it's an inflection point. So what we're going to do is, we're going to find all of the points at which this is true, and then see if we actually do have a sign change in the second derivative at that point. And only if you have a sign change, then you can say it's an inflection point.