 
Summary: ROOTFINDING : A PRINCIPLE
We want to find the root of a given function f(x).
Thus we want to find the point x at which the graph of
y = f(x) intersects the xaxis. One of the principles
of numerical analysis is the following.
If you cannot solve the given problem, then solve a
"nearby problem".
How do we obtain a nearby problem for f(x) = 0?
Begin first by asking for types of problems which we
can solve easily. At the top of the list should be that
of finding where a straight line intersects the xaxis.
Thus we seek to replace f(x) = 0 by that of solv
ing p(x) = 0 for some linear polynomial p(x) that
approximates f(x) in the vicinity of the root .
(x
0
,f(x
0
))
x
