Something interesting here. Your second derivative is 0 when x is equal to 0, but it is not an inflection point, because notice the concavity did not change around 0. Our second derivative is positive as we approach 0 from the left, and it's positive as we approach 0 from the right. In general, at 0, as we're near 0 from either direction, we're going to be concave upwards. The fact that 0 is a critical point, and that we're always concave upward as we approach 0 from either side, this tells us that this is a minimum point. Because we're concave upwards all around 0. 0 is not an inflection point.