So those are the different candidates. Now you could have a critical number in between where, say, the slope is zero, say something like this, but it isn't the maximum or minimum. But what we can do is if we can find all the critical numbers, we can then test the function evaluated at the critical numbers and the function evaluated at the endpoints, and we can see which of those are the largest. All of those are the possible candidates for where f hits a maximum value. So first we could think about, well, actually, let's find the critical numbers first since we have to do it. So let's take the derivative of f. f prime of x is going to be equal to the derivative of natural log of x is 1 over x. So it's going to be 8 over x minus 2x.