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)

Question

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)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

lather, rinse repeat
it gets real messy real fast

anonymous · Answer

I'm kind of remembering how to do this

anonymous · Answer

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

anonymous · Answer

Thank you very much for your help :)

anonymous · Answer

yw