And now let's look at the graph of this to feel good about what we just did analytically without looking at it graphically. And I looked at it ahead of time. So let me copy and paste it. And so this is the graph of our function. So as we can see, when this point right over here, this is when, this is one over the square root of e. It's not obvious from looking at it that it's that point. X equals one over the square root of e. And we can see that it is indeed an absolute minimum point here. And there is no absolute maximum point.