00:01
We are going to calculate two iterations of newton's method for the function f of x equal x squared minus 8 using the initial guess x1 equal 2.
00:13
And we are going to complete this table here.
00:18
So the first thing we have to do because we use it in newton's method is calculate the derivative of f.
00:25
Derivative of f in this case is a polynomial function derivative of x square is 2x plus the derivative of negative 80 is 0 so we get 2x that so we have that and now we start calculating so x1 is 2 and for n equal 1 here in this column we are talking about x1 and we know that's the initial guess 2 then the function at 2 will be this formula for x equal 2.
01:00
So we get 2 squared is 4 minus 8 is negative 4.
01:04
Now the derivative at x1, that is at 2, is this formula evaluated at x equal 2.
01:15
So we get 4.
01:17
Now the quotient of this column is divided by this other column here is negative 4 over 4.
01:26
What is the same is negative 1.
01:30
And now this operation here, which give us xn plus 1, that is the next hit rate, which is x2, which will put the result here we are going to put in this column in the second row.
01:46
But now we calculate that.
01:48
So the calculation we got to do is x1 minus the quotient f at x1 over the derivative at x1.
01:57
And that will give us x2.
02:00
As you can see, is the value of this column minus the value of this caution here.
02:06
So it's 2 here minus the value here in this column, the caution, negative 1, and that is 2 plus 1, that is 3.
02:18
And that value is x2...