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

.