Newton's Method on a Mesh of Initial Guesses

c

3

1.2

c

2

1.76

c

1

-3.22

c

0

-5

featured initial guess

0

0 iterates to 1.66049

This Demonstration shows the path of 50 iterations of Newton's method from a mesh of starting points attempting to solve the cubic equation

c

3

x

+

c

2

x

+

c

1

x+

c

0

=0

. A "featured" initial guess is highlighted in blue. If the absolute value of

f'(x)

is less than

-5

10

, no iteration is taken.