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. So let's see if we can do that. So just because the second derivative is 0, that by itself does not tell you it's an inflection point. It has to have a second derivative of 0, and when you go below that x, the second derivative has to actually change signs.