... for finding the zeros of a smooth function.
[i]Begin[/i]
[math] \;\;\;[/math] Choose a point at pleasure on the curve, [math] {\small P_0 = (x_0, f(x_0)) }[/math] and
[math]\;\;\;[/math] Draw the tangent to the curve at [math] {\small P_0}[/math].
[math]\;\;\;[/math] Mark the intersection with the x-axis, [math] {\small X_1 = (x_1, 0)} [/math].
Let this be the new x-value.
[math]\;\;\;[/math] Mark [math]{\small P_1 = (x_1, f(x_1)) }[/math] on the curve.
[math]\;\;\;[/math] Draw the tangent to the curve at [math] {\small P_1}[/math].
[math]\;\;\;[/math] . . .
The sequence converges to a real zero of f(x).
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As always, these are my self-study materials. Let me know how I can make them more useful to you.
