If you have a differentiable function f and you want to calculate a zero of f then you need first a guess (usually called ) which value of x will give f(x) near zero. Then you can start an iterating process to get an approximative value of the zero by:

If you take the commands and keep in mind that the sign ">" means "store":

N+1>N..... The counter increases by 1 and is stored in the variable N

X-y1(x)/y2(x)>x..... Calculate the next value of x and store the value in the variable X. It is necessary here that f(x) is stored in y1(x) and f'(x) in y2(x).

{N,X,Y1(x)}..... Collect all results in a list so the output can be organized much easier.

By the way: With this program it is absolutely necessary to define a condition which ends the calculations. Otherwise your calculator will be caught in an endless loop.