Julia Sets and the Mandelbrot Set
Real Newton's Method
Derivation of the Newton's Method Formula
We derive the relation between x
1
and x
0
; the others are similar.
Note the points
(x
0
, f(x
0
))
and
(x
1
, 0)
lie on the line tangent to the graph of y = f(x) at the point
(x
0
, f(x
0
)).
The slope of the tangent line is
f '(x
0
),
so we have
f '(x
0
) = (f(x
0
) - 0) / (x
0
- x
1
)
Solving this for x
1
gives
x
1
= x
0
- f(x
0
)/f '(x
0
)
Return to
real Newton's Method
