Posted by **Andres** on Thursday, November 17, 2011 at 12:04am.

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.

- Calculus -
**Reiny**, Thursday, November 17, 2011 at 12:32am
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 !!!!

- Calculus -
**No Name**, Thursday, November 17, 2011 at 2:02pm
What is this newx and how did you get the equation that says x-y/y'

- Calculus -
**Reiny**, Friday, November 18, 2011 at 5:20pm
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?

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