Let's see if what we just established is actually consistent with what the graph actually looks like. We were able to come up with these insights about the concavity without graphing it. But now it's kind of satisfying to take a look at a graph. And actually let me see if I can match up the intervals. So actually this is pretty closely matched right over here. And so this is, actually let me make it a little bit smaller, all right. And so let me move my bounding box.