00:01
Okay, so i'm going to try to sketch this graph and illustrate what happens when you start newton's method with all these points.
00:11
So let's just plot the relevant points that we have zero, one, two, three, four.
00:32
Keep going a little bit.
00:40
A little bit more real estate over here.
00:44
So there's five.
00:47
One, two, three.
00:51
Okay, so we're going to go up and then down, level off, and then we'll go down, like that.
01:26
So hopefully you'll get the idea when i just do a couple of these.
01:30
So let's say we start at zero.
01:32
So newton's method is going to say, okay, well, the first point, the first approximation of the root is going to be here.
01:41
And then what we do is we basically find the equation of the tammation.
01:46
Tangent line at that point.
01:50
So here's our first x0 being zero.
01:55
And then here's going to be x1.
01:57
It's going to be the zero of the linearization of the function at that point.
02:02
And then we go up.
02:04
And then there's our function value.
02:06
And so then we'll find the tangent line again.
02:12
And then here will be x2.
02:15
Then we'll go again.
02:17
And so you see what's happening.
02:19
These tangent lines are going to be leveling off to zero and the the x values are going to be going off to minus infinity so for x equals zero so that's a so let's write down what all we need to do a b c d e so we're starting at zero zero is one two oops x zero is two one x zero is two one x zero is two one x zero two two x0 is 4, and x0 is 5 .5 .5.
03:13
Okay, so x0, we're going to go to minus infinity...