Edexcel C3 Iteration help please

I'm self studying C3 and am looking through the Edexcel textbook. I'm up to Iteration and I'm aware of the idea that an iterative formula can cause the answer to diverge away from the solution.

However, on the mixed excercise in the textbook, you get an interval and are asked to use iteration to approximate a root. What should I use as my first value of x from the interval? Do I just take the middle value or is it trial and error so that it doesn't diverge?

Any help would be appreciated

If they give you an interval to start iteration from, then surely it is an interval from which successive iterations will converge onto the root...?

Yeah, but say the interval is (3,4), I don't know what to take as my first value of x to substitute into the iterative formula. Is it 3? 3.5? 4? Or anything in between?

Well my last post implies that its anything in between in this case.

That's what I originally thought, but the answer page in the text book has specific answers for each successive iteration. I don't know whether to take them with a pinch of salt? Because the answer you get is obviously going to vary by a tiny amount depending on what you pick as your starting value (say you pick 3.5 instead of 3).

Yes your final iteration would be just SLIGHTLY ever so different depending on what starting value you pick, but should be correct to like 2 decimal places in most cases.

Anyway, as long as you converge onto the same root as the mark scheme, you get the mark.