define
Find .
Hence evaluate
for .
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)= ???
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.