## jossy04 Group Title 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) 11 months ago 11 months ago

1. satellite73 Group Title

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

2. satellite73 Group Title

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

3. satellite73 Group Title

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

4. satellite73 Group Title

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

5. satellite73 Group Title

lather, rinse repeat it gets real messy real fast

6. jossy04 Group Title

I'm kind of remembering how to do this

7. satellite73 Group Title

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 Group Title

Thank you very much for your help :)

9. satellite73 Group Title

yw