WOLFRAM|DEMONSTRATIONS PROJECT

Two Geometric Views of Newton's Method

​
x0
n
0
1
2
3
4
5
The top plot shows the usual geometric picture of Newton's method for finding an approximate solution to
f(x)=0
. Starting with an initial guess,
x
0
​
, move down the tangent until you hit the
x
axis, then calculate a new tangent line and repeat
n
times. The bottom plot is a cobweb plot for
g(x)=x-
f(x)
f'(x)
. This illustrates that Newton's method composes
g(x)
with itself
n
times starting with
x
0
.