## anonymous 2 years 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. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

lather, rinse repeat it gets real messy real fast

6. anonymous

I'm kind of remembering how to do this

7. anonymous

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. anonymous

Thank you very much for your help :)

9. anonymous

yw