Question

Use Newton's method to approximate a root of the equation 3x^7+4x^4+3=0 as follows.
Let x1=3 be the initial approximation.

whats x2 and x3?

Answer 1

This kind of problem its quite simple.
You just need to look up the formula - I had to look it up myself in my formulary.
\[x_{T}=x _{1}-f(x _{1})/f`(x _{1})\]
So you need to calculate the first derivative and than start with x _{1} = 3 than you get and new x2. Than you plug than again into the equation and get this a way a x3 and than you have your approximiation.