and  intersect
at  , then:
the iterative process 
converges to
if  . |
Activities
Numerical methods of solving equations - Newton's method - Why it is so good?
As mentioned in "When will a sequence
converge to a solution?" (sequence
graphs and web plots):
|
and intersect
at , then:
the iterative process
converges to
if . |
In Newton's method 
.
Find 
and show that
where
is a solution to the equation 
.