# Math Help - Newton's method

1. ## Newton's method

I dont know what they want me to do!! and I dunno how to do it!

To solve the equation

by Newton's Method we start with a good initial guess and then run the iteration

until we get an approximation that is good enough for our purposes.

Suppose you want to compute the cube root of 4 by solving the equation

Since and Let's start with

Then
,
,
, and
To check your answer compute .

2. in this specific exercise f(x) = x^3 - 4
Newton's method is an algorithm for finding the zeros of a function, you can find more information about it here:

http://en.wikipedia.org/wiki/Newton's_method

it's an iterative method and we need to come up with an initial guess the closer to the zero the better, in this example the Intermediate Value Theorem is used to choose the initial guess, now we have to calculate f '(x)
f ' (x) = 3*x^2

Xn+1 = Xn - ((Xn)^3 - 4) / (3*(Xn)^2)
Xo = 1.5
so:

X1 = Xo - ((Xo)^3 - 4) / (3*(Xo)^2) = 1.5925

X2 = X1 - ((X1)^3 - 4) / (3*(X1)^2)......