This method should converge to the nearest root if a close enough starting point is choosen.
Maybe your derivative is wrong? Maybe your calculations are out? Are you doing them by hand or using technology?
so I have a cubic equation here with 3 roots I need to find using newtons method. Basically I wanted to know how to determine the starting point. I picked an x value close to the root from what I can tell on the graph but newtons method keeps giving me larger numbers and then smaller numbers on each recursion.
That is quite possible. Pick a different one. Without the actual function, it's a bit difficult to say where one might have failed at the process.
Starting closer is one possible solution. Given some bound on the solution, perhaps given by the failed Newton, ry a bisection or two and then go back to Newton, since the exercise seems to demand it.
I already know the roots, for example one of them is ~-1.7, I picked -2 as a starting point but the recursion isn't getting me anywhere.
so basically I started with
-2 - f(-2)/f'(-2)
and then use that value as my new x