00:02
Before we actually start doing the bisection method, let's kind of go through what it actually is.
00:07
So we have these two initial guesses, x is equal to zero and x is equal to one.
00:11
So let's just kind of plot these over here with us.
00:13
So this is x is equal to zero and this is x is equal to one.
00:17
So you might notice that x is equal to zero gives a negative output, while x is equal to one gives a positive output.
00:24
So since this is a continuous function or really just as a polynomial, we know there has to be some zero in between these.
00:34
So one way we can go about making a guess is just by taking the average of those input.
00:39
So it would be 0 and 1's average is a half, so a half is around like right here.
00:46
So this is where that would be on the graph.
00:50
Well, now this is a positive output.
00:53
So what we can do is average that x value with the closest one that gives a negative output to it, which in this case would be 0.
01:02
So we do a half and zero and average it to get a fourth.
01:08
So that would be around like right here.
01:12
Now this is a negative output.
01:14
So then we would want to average the input with the negative or the positive closest to it, which is going to be one half.
01:25
So we average a half and a fourth and we get something around like right here, which you can see really close to the solution.
01:35
So that's the idea behind what we're going to be doing.
01:38
So first let's go ahead and find f of 0 and f of 1.
01:42
F of 0 is going to be negative 2.
01:45
F of 1 is going to be 4.
01:48
And i already went ahead and plug these in.
01:52
So i'm just trying them down.
01:55
Now, because we have this change aside, we can go ahead and get our new x value.
02:00
So we can say that x1 is going to be equal to this average of 0 and 1...