Question

# PROBLEM to apply Newton's Root Approximation Method to.

Consider the functions g(x)

= x^{3} ; 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, calculate up to x_{3} value.

B. Your title should include YOUR NAME: Newton

C. Naturally, I am also looking for a use able URL as well.

D. A graph zooming in on the point of intersection would be excellent as well.

SOLUTION: Set

Call the new function f(x)=

x value f'(x)= x[n] - {f(x) / f'(x)}

f(x)= x[n+1]=x[n]-f(x[n]) /f '(x[n])

ti-84 L1 L2 L3 L4 __L1 - L4 ... L5__

__ n__ __x[n] ... L__ __f(x[n])__ __f ' (x[n]) __ __f(x[n])/f ' (x[n]) = y3__ New guess

__= y1 ... L2__ __= y2 ... L3__ __= y1/y2 ..L4__

1 1

2

3 Final Solution

Include a URL

#### Top Answer

g(x) = x 3 h(x) = -3x + 6 g(x) = h(x) x 3 =+ 6 = 0 or , x 3 + 3 x - 6 = 0 f(x) = x 3 + 3 x - 6 f'(x) = 3 x 2 + 3 x 1 = 1 ,... View the full answer