» Required Reading » Table of Contents » Chapter 3: Vectors, Dot Products, Matrix Multiplication and Distance 12.3 Spreadsheet Implementation of this Procedure
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How can you do such things?
First put x and j in fixed locations X and Y.
Then set up the following columns on the spreadsheet:
f(x_j):
In the first column enter the successive values of f(x_j) starting with the first, known value. For roots you can start with x₀  = f(x₀) = 1. Compute later values f(x_j) by using the linear approximation tangent line at x_j-1 evaluated at argument x
x_j:
In the second column apply the inverse function to f to the value in the previous column.
Once you have entered your instructions for f(x₁) and x₁, you can copy these down a hundred rows, and you are done.

How do I use  the linear approximation as required above?
Here is what to do for roots: the linear approximation will read:

f(x₁) =  f(x) = f(x₀) + (x - x₀)f '(x₀).

 For jth root,  f '(x₀) = f(x₀) / x₀ / j so that this formula reduces to:

f(x₁) = f(x) = f(x₀)(1- (1/j) + (x / j / x₀)).