Perhaps the most widely used of all root-locating
formulas is the Newton-Raphson equation.
If the initial guess at the root is Xi. a tangent can
be extended from the point [Xi,f(Xi)].
The point where this tangent crosses the x
axis usually represents an improved estimate of the root
The Newton-Raphson method can be derived on the basis
of this geometrical interpretation (an alternative method based on the Taylor
series). As in the first derivative al x is equivalent to the slope:
This can be rearranged
to yield
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