The graphs of f(x) = x^3 and g(x) = 3X+5 have one intersection point. Determine the x-value 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.

Answer 1

To find the intersection point, set
x^3 = 3x+5
x^3-3x-5 = 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^3-3)

Using my calculator
x1 = 21/9 = 2.333333
x2 = 2.28055555
x3 = 2.27902
x4 = 2.27902 --- correct to 5 decimal places !!!!

Answer 2

What is this newx and how did you get the equation that says x-y/y'

Answer 3

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?