1. ## newtons method

Use Newton's method to approximate the root of the equation

x^3=113 x+226

that belongs to the interval (6,12 ).

Start with x0=12 and perform three iterations, i.e., find x1,x2, and x3.

Calculate |x0−x1|,|x1−x2|, and |x3−x2|.

1. Use Newton's method

where the function f has a positive leading coefficient so that f(x)= ???

2. define $f(x)=x^3-113x-226=0$

Find $f'(x)$.

Hence evaluate

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$ for $n=0,1,2$.

3. Use the equations right?
So x1=12-[f(12)/f'(12)], then x2=x1-[f(x1)/f'(x1)] and so on..
Is that what you were asking for?
With
f(x)=-x^3+113x+226
f'(x)=-3x^2+113
Then it's just simple substitution from there.

4. Originally Posted by endling
Use the equations right?
So x1=12-[f(12)/f'(12)], then x2=x1-[f(x1)/f'(x1)] and so on..
Corrections in red.

5. Originally Posted by scorpion007
Corrections in red.
Oh, sorry, yes, you are correct. It's a bit late into the evening for me x___x

6. thank you both so much, i got it now