Question about tutorial 6 Q6 - Interval for newton convergence

[kuriant1]

Hello!
I am referring to page 13 in tut-06

Over here, is there a reason why we started the interval from 2 instead of (16/5) ^ {1/3} + sm small no = 1.4736 + small no?

If I’m not wrong, g still maps the interval [1.4736 + small no, inf) to [1.4736 + small no, inf) because g is decreasing from x = 1.4736 to x = 2 where u get a minima with value g(2) = 2.
So, between x in [1.4736 + delta, 2), your function g(x) starts at value g(1.4736) = 2.21, goes to 2 and starts increasing to infinity. Aaand this is still within the range [1.4736 + small no, inf)

And more specifically, g(x) in [2, inf) subset of [1.4736 + delta, inf)
So delta <= 0.5264

Is what I said correct?

Thanks!

[ccc]

Yes, it is correct, but there is nothing wrong with the solution given in tut06.
You have that g(x) is in [2, inf) which is subset of [1.47… + delta, inf).
The self-map property can be a mapping to a subset.