SOLUTION: PROBLEM to apply Newton's Root Approximation Method to. Consider the functions g(x) = x3 ; h(x) = -3x+6 Apply Newton's Method to approximate x value intersection of these two g

Question 1132516: PROBLEM to apply Newton's Root Approximation Method to.
Consider the functions g(x) = x3 ; h(x) = -3x+6
Apply Newton's Method to approximate x value intersection of these two graphs.
A. Please begin your first guess of x 1 = 1,ca lculate up to x3 value.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
g(x) = h(x)
:
g(x) - h(x) = 0
:
1) x^3 +3x -6 = 0
:
We want to solve equation 1 for values of x using Newton's Method
:
Newton's Method says
:
x(n+1) = x(n) - f(x(n))/f'(x(n))
:
we begin with x(1) = 1
:
Note f'(x) = 3x^2 +3
:
x(1) = 1 -(-2)/6 = 1 +(1/3) = 4/3 = 1.3333
:
x(2) = 1.3333 -(0.3701/8.3331) = 1.2889
:
x(3) = 1.2889 -(0.0079/7.9838) = 1.2879
:
***********************************************************************
Turns out that 1.2879 is a good approximation for the intersection
:
usually we stop the iterations when the difference of two iterations is
less than 0.0001
***********************************************************************
:

RELATED QUESTIONS
Use Newton�s method in 2 steps to solve the equation {{{log(x + 2) = e x − 2}}} for (answered by Fombitz)

You want to approximate the cube root of 7 using the Newton-Raphson method. First,... (answered by Alan3354)

By using the Newton-Raphson�s method find the root of the quadratic equation X^3+logx... (answered by Fombitz)

If f(x) = x^3 - 2x and Xo = 2 is initial approximatio. What is the next approximation to (answered by Solver92311)

3. By using the Newton-Raphson�s method find the positive root of the quadratic equation (answered by Edwin McCravy)

How to differentiate the equation to find f'(x) to work it out using the Newton-Raphson... (answered by solver91311)

use newton's method to determine the positive root of the quadratic question... (answered by ikleyn)

Apply the delta method to find derivatives of the following problem: f(x)=... (answered by Alan3354)

Find a root of an equation f(x)=2coshxsinx-1 taking initial value x0=0.4, using Newton... (answered by ikleyn)