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Summary: THE SECANT METHOD
Newton's method was based on using the line tangent
to the curve of y = f(x), with the point of tangency
(x0, f(x0)). When x0 , the graph of the tangent
line is approximately the same as the graph of y =
f(x) around x = . We then used the root of the
tangent line to approximate .
Consider using an approximating line based on `inter-
polation'. We assume we have two estimates of the
root , say x0 and x1. Then we produce a linear
function
q(x) = a0 + a1x
with
q(x0) = f(x0), q(x1) = f(x1) (*)
This line is sometimes called a secant line. Its equa-
tion is given by
q(x) =
(x1 - x) f(x0) + (x - x0) f(x1)
x1 - x0
(x
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