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The function whose graph is drawn is a cubic of the form:
y = Ax3 + Bx2 +
Cx + D, and you can vary this function by dragging the
A, B, C and D sliders at the bottom.
The Newton-Raphson Method involves the iterative formula:
xn + 1 = xn - f(xn)/f '(xn)
which is used to try to solve the equation f(x) = 0.
The starting value for the iteration is represented by the light blue
circle drawn on the x-axis. This circle can be dragged left and
right with the mouse, to see how the iteration depends on the starting value.
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You can also vary the number of iterations performed. The slider at the top right changes the number of iterations rapidly, but you can use the "Iter+" and "Iter-" buttons at the very top to change the number of iterations one at a time.
The program enables you to investigate how this iteration converges to a solution to the equation (if it does!), which solution is found (if any), and how quickly or slowly the convergence happens.
Play around - there are some fascinating patterns to observe!
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