00:01
This problem wants us to use the intermediate value theorem to find an interval of length, one half, to find that there's a root on xq plus 2x plus 1 that is in that interval of this length.
00:12
So we know that the intermediate value theorem states that if we have a closed and continuous interval, that the values of the endpoints that we get from plugging in the endpoints, that there's got to be a value in between those values, that there's a point at f of x that will.
00:30
Reach that value.
00:30
And that sounds really confusing just saying it, so it's much easier if we really just do the problem out.
00:35
So we have xc plus 2x plus 1, and we want it to equal 0 because we want to find the root.
00:40
But we need to find our interval first, and it has to be length of 1 half.
00:44
So what we can do is we can test out an interval of 0 and we'll just say 1ā2.
00:52
But we can see that we quickly run into problems, because if we first test out x equals 0, then we get 0 plus 0 plus 1.
01:01
We get 1.
01:03
But if we test out 1 half, we get 1 half cubed plus 2 times 1ā2 times 1ā2 plus 1.
01:07
So that's still a positive number.
01:09
It doesn't really matter what we get.
01:11
We can do it out, but it's a positive number...