Calculus
posted by Andres .
The graphs of f(x) = x^3 and g(x) = 3X+5 have one intersection point. Determine the xvalue for this intersection point using Newton's Method with an initial estimate of X1=2. You should use this method three times in order to obtain estimates X2, X3, and X4.

To find the intersection point, set
x^3 = 3x+5
x^33x5 = 0
let y = x^3  3x + 5
dy/dx = 3x^2  3
newx = x  y/y' = x  (x^3  3x  5)/(3x^2  3)
= (2x^3 + 5)/(3x^33)
Using my calculator
x1 = 21/9 = 2.333333
x2 = 2.28055555
x3 = 2.27902
x4 = 2.27902  correct to 5 decimal places !!!! 
What is this newx and how did you get the equation that says xy/y'

Your problem says to use Newton's Method
I stated the formula for Newton's Method.
Are you in over your head for this question?