00:01
Okay, so we're using the bisection method to find the root for f of x is equal to x to the fifth minus x3.
00:09
So we'll start with our number line of x values from 1 to 3.
00:13
And our first bisection will give us n0.
00:19
So our n0 will be at the x value that is halfway between 1 and 3.
00:25
So we'll take 3 plus 1, divide by 2, to give us a value of 2.
00:30
And this is where our n0 is going to be equal to, which is the x value here.
00:36
So then we're going to plug in our endpoints to our function.
00:41
So f of 1 is going to be 1 minus 3, which is negative 2.
00:46
So we know that the y value here is negative.
00:49
Then our f of 3 is going to be 3 to the 5th minus 3 times 3, which is 9.
00:54
And it's going to give us a positive value at this endpoint.
00:58
So we know the 0 exists between them.
01:00
Now if we plug in our n0 or 2, we also get a positive value here.
01:07
So now we know the 0 exists between 1 and n0...