00:01
Okay, we want to find a root of this equation, or we want to show that there is one in the interval from 2 to 3 using the intermediate value theorem.
00:10
So root usually means the value of some function is 0.
00:13
We actually don't have that, so we have to make that.
00:15
Let's make the function natural log of x minus x plus root x.
00:21
Because if that were zero, then this equation would be true, right? we can get from there to that equals 0 by adding or subtracting stuff from both.
00:30
Sides.
00:32
Okay, so we have that.
00:34
Let's look at this function is defined on the endpoints.
00:38
Natural log is defined for two and three.
00:40
So let's look at the values of f of 2 and f of 3.
00:46
And because we have a natural log, we need a calculator.
00:50
I'm not going to be able to show that on the screen because i don't have a good computer calculator...