## jossy04 one year ago How does newton's method work ? This is all supposed to be a review, but I'm having trouble remembering how it works... f(x)=x^3 + x + 3 (Initial Guess = 1)

1. satellite73

$x_{n+1}=x_{n}-\frac{f(x_n)}{f'(x_n)}$

2. satellite73

first guess is 1 $$f(1)=5$$ so $$1$$ is kind of a lousy guess, since you want it to be 0

3. satellite73

$f'(x)=3x^2+1$ so $f'(1)=4$

4. satellite73

second guess is therefore $$x_2=1-\frac{5}{4}=-\frac{1}{4}$$

5. satellite73

lather, rinse repeat it gets real messy real fast

6. jossy04

I'm kind of remembering how to do this

7. satellite73

you can also do some algebra if you like before you start $x-\frac{f(x)}{f'(x)}=x-\frac{x^3+x+3}{3x^2+1}$ $=\frac{2x^3-3}{3x^2+1}$ and plug in there, but it amounts to the same thing

8. jossy04

Thank you very much for your help :)

9. satellite73

yw