00:01
For this problem we are asked to perform three iterations of the function, negative 0 .9x squared plus 1 .7x plus 2 .5, using the fixed point iteration and newton -rapson method, starting with x -0 equal to 3.
00:18
Now for the fixed -point iteration, the first step will be to convert f -of -x equals 0 into the form x equals g of x.
00:29
So if i have negative 0 .9x squared plus 1 .7x plus 2 .5, we set this to 0 .5.
00:38
We'll have negative 0 .9x squared plus 1 .7x.
00:43
That's equal to negative 2 .5.
00:46
We factor out an x.
00:48
We have x times negative 0 .9x plus 1 .7.
00:54
That's equal to negative 2 .5.
00:56
So our x will be equal to negative 2 .5 over negative 0 .9x plus 1 .7.
01:06
That's the same as 2 .5 over 0 .9x plus or minus 1 .7.
01:14
And then you will use this to do our iteration.
01:18
And here we want to do x sub i plus 1.
01:22
That's equal to g of x sub i.
01:26
So starting with i equals 0, we have x of or x sub 1, that's equal to g of x of 0.
01:38
And since our x of 0 is 3, then this will be 2 .5 over 0 .9 times 3 minus 1 .7, that's equal to 2 .5...