@Rouben Rostamian  

it is unfortunately a requirement for the question I've been given..

@Carl Love 

yeah the formula for the iterator is exactly what's on Cheney and Kincaid Numerical Methods 6th edition; and the next step is to write similar code for the Halley's method. What I am clueless about is how to structure the recurrence relation for a function of my choice

@Carl Love 

sorry, the function was x(x-1)^3

I realized my error,thanks

@Carl Love 

changing g to a regular expression doesnt seem to work either

@Carl Love 

I'm using maple 18; here's what I've tried:

g:=(x,y)->(x^3)+(y^3)-1;
d1:=implicitdiff(g(x,y),y(x),x);
d2:=implicitdiff(d1,y(x),x);
plots:-implicitplot(x^3+y^3=1,x=-5..5,y=-5..5,gridrefine=3);

and the error is the same as before:

Error, invalid input: implicitdiff expects its 2nd argument, yx, to be of type {name, set(name), set(function(name)), function(name)}, but received x^3+y^3-1
Error, invalid input: implicitdiff expects its 2nd argument, yx, to be of type {name, set(name), set(function(name)), function(name)}, but received x^3+y^3-1

@Kitonum 

Thanks Kitonum! If I were to compute the derivatives at points where it existed, how would I do so?