need help! using newton's method

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
Hi,

I assume that you know Newton's rule.
\(\displaystyle x_{n+1}=x_{n}-\frac{f(x_n)}{f'(x_n)}\)

With your function this formula becomes:

\(\displaystyle x_{n+1}=x_{n}-\frac{x_n^3-x_n^2-1}{3x_n^2-2x_n}\)

Now \(\displaystyle x_1 = 1\). Thus

\(\displaystyle x_{2}=1-\frac{1-1-1}{3-2}= 2\)

\(\displaystyle x_{3}=2-\frac{8-4-1}{12-4}= 1.625\)

...

\(\displaystyle x_{7}\approx 1.465571232\)

EB
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
Hi, it's me again. I've modified your image so you can see the first steps how the value is calculated by Newton's method. The red and blue lines are tangents.
 

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