What seems to be the trouble?. Newton's Method is one of the easiest things in calculus.

It's just a matter of iterations.

Let's give an example:

Use Newton to find the 'real' solutions of

Let

Graph the function,

You can see that y=0 when x is between 1 and 2.

Make something in that region your initial guess.

Try 1.5

Now use the result you get from this and sub back into the equation:

What is wrong with this website that I keep getting these errors saying the image is too big?. I've never seen this on another site. The code is fine as far as I can tell..

Continue in this fashion until you arrive at approximations which are so close they are virtually unchanged.

We end up with:

See, the last two are the same.

No need to continue. . The solution is