Newton Method, please help me

Question

Consider the following -2x^5+9x^4− 7x³ − 14x = 0,    [3, 4]

Use Newton's method to approximate the solution correct to six decimal places.

I know how to solve the problem with the Newton method, but it's quite complicated to calculate. So how can I find this value? Is there any way to solve the newton method easily?

Answer 1

I did this in Desmos very quickly because I had done the others.

Let f(x) be the Left Hand Side, g(x) = x - f(x)/f'(x). Use table to iterate the calculations.

I'm sure I've got it down to easiest method (or almost easiest).

I got 3.1837648 or to six decimals 3.183765

Hope this helps.

Answer 2

3.18376

whoops, only 5 decimals

well, if that was rounded, then

that narrows it down to

either

3.183755

3.183756

3.183757

3.183758

or

3.183759

you have a 1 int 5 or 20% chance of getting it right for full credit

maybe partial credit

to get closest try the midpoint with least error: 3.183757

at worst it's two digits off? very close, even at worst?