00:01
In this question, we're going to find all the critical points for the function f of x equals x minus ln x, and then the absolute maximum and minimum values of f on the interval.
00:11
So let's start by getting our critical points.
00:13
Let's get f prime of x.
00:15
My f prime of x this time is 1 minus 1 over x.
00:20
Now my f prime is never undefined, so let's focus on figuring out where f prime equals 0.
00:31
I'm going to have 1 minus 1 over x equals 0.
00:35
I'm going to add 1 over x to each side, and then i multiply by x.
00:42
I'm getting x equals 1.
00:45
So x equals 1 is going to be my critical number.
00:51
And that's the only critical, critical value or critical number.
00:59
Now, i'm on a closed interval.
01:01
So what do i do? i evaluate f at my critical points and my endpoints.
01:08
So i'm going to evaluate f of 1 half, f of 1, and f of 3.
01:17
Now, f of 1 half would be 1 half minus the natural log of 1 half...