Use Newton's method with initial approximation
x1 = 1
to find x2, the second approximation to the root of the equation
x4 − x − 8 = 0.
I worked it out and got 3.6666667 but it was wrong, please help!

Question

Use Newton's method with initial approximation
x1 = 1
to find x2, the second approximation to the root of the equation
x4 − x − 8 = 0.
I worked it out and got 3.6666667 but it was wrong, please help!

jim_thompson5910 · Answer

Newton's Method

$$\Large x_{n+1} = x_n - \frac{f(x_n)}{f \ '(x_n)}$$

jim_thompson5910 · Answer

If n = 1, then

$$\Large x_{n+1} = x_n - \frac{f(x_n)}{f \ '(x_n)}$$
$$\Large x_{1+1} = x_1 - \frac{f(x_1)}{f \ '(x_1)}$$
$$\Large x_{2} = 1 - \frac{f(1)}{f \ '(1)}$$

So you need to compute both f(1) and f ' (1). Do you know how to do that?

anonymous · Answer

yeah, i worked everything out i got x^4-x-8/4x^3-1 and I plugged in 1 for the x and then got -8/3, then i did 1-(-8/3) and got 3.66667?

jim_thompson5910 · Answer

Yeah I'm getting that too. Maybe they want you to round a very specific way?

jim_thompson5910 · Answer

I doubt they want it as a fraction, but who knows really.

anonymous · Answer

that's what i was thinking, that maybe they wanted it in fraction form, but it doesn't specify...

jim_thompson5910 · Answer

I've never seen newton's method approximations as fractions. Usually they are in decimal form. Can you post a screenshot of the full problem?

anonymous · Answer

Use Newton's method with initial approximation
x1 = 1
to find x2, the second approximation to the root of the equation
x4 − x − 8 = 0.

x2 =3.67 Incorrect: Your answer is incorrect.

anonymous · Answer

That's all of it

jim_thompson5910 · Answer

Hmm so odd and frustrating. It would be nice if they added "round to 5 decimal places" or something.

anonymous · Answer

exactly! and i only have two tries so im scared to use my last one and get it wrong, since i dont know how im supposed to type the answer

jim_thompson5910 · Answer

The only thing you can do really is look back at previous correct problems to see what the computer wants. Or try to guess it anyway.

jim_thompson5910 · Answer

Or ask the teacher. I would ask for points back if you get it wrong since this problem is unfair.

anonymous · Answer

yeah I'll try to do that, thanks for checking my answer though!

jim_thompson5910 · Answer

no problem

anonymous · Answer

it was in fraction form lol

jim_thompson5910 · Answer

so strange, but I guess computers tend to be that way