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!

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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!

Calculus1
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Newton's Method \[\Large x_{n+1} = x_n - \frac{f(x_n)}{f \ '(x_n)}\]
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?
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?

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Yeah I'm getting that too. Maybe they want you to round a very specific way?
I doubt they want it as a fraction, but who knows really.
that's what i was thinking, that maybe they wanted it in fraction form, but it doesn't specify...
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?
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.
That's all of it
Hmm so odd and frustrating. It would be nice if they added "round to 5 decimal places" or something.
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
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.
Or ask the teacher. I would ask for points back if you get it wrong since this problem is unfair.
yeah I'll try to do that, thanks for checking my answer though!
no problem
it was in fraction form lol
so strange, but I guess computers tend to be that way

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