Newtons method to estimate solution to eq.

[Ashleyz]

Homework Statement

Use Newton's method to estimate the requested solution of the equation. Start with given value of x0 and give x2 as the estimated solution.

Homework Equations

x0 = 2 ( this is the first guess numb. you start with)
the equation you use is... x = x(guuess #) - f(xg)/f'(xg)

f(x) = x^4 -6x +3 and f'(x) = 4(x)^3 -6

The Attempt at a Solution

I have done the entire problem. several times.
when x ='s 2, I got 1. 731

when x ='s 1.731 I got 1.623

when x ='s 1.623 I got 1.604 for my final answer.

perhaps this answer is correct , and the multiple choice answer is wrong.

If you are familiar with Newtons method- then this won't take too long for you.
You just plug and chug.

 

[Pacopag]

Your answer is right. The next digits are
1.604439
I just punched into maple and got this answer.

 

[HallsofIvy]

Homework Statement

Use Newton's method to estimate the requested solution of the equation. Start with given value of x0 and give x2 as the estimated solution.

Homework Equations

x0 = 2 ( this is the first guess numb. you start with)
the equation you use is... x = x(guuess #) - f(xg)/f'(xg)

f(x) = x^4 -6x +3 and f'(x) = 4(x)^3 -6

The Attempt at a Solution

I have done the entire problem. several times.
when x ='s 2, I got 1. 731

when x ='s 1.731 I got 1.623

when x ='s 1.623 I got 1.604 for my final answer.

perhaps this answer is correct , and the multiple choice answer is wrong.

If you are familiar with Newtons method- then this won't take too long for you.
You just plug and chug.

That is correct to three decimal places. What are the choices?

 

[gabbagabbahey]

Wouldn't that give you x_0=2 , x_1 \approx 1.731, x_2 \approx 1.623 and x_3 \approx 1.605?

soo if you are asked to find x2...would that not be 1.623?

 

[Ashleyz]

my full answer is 1.604938639

when pluging the answers back into the equation and dividing
by the derrivative, I only was tacking my answer to 3 decimal places
keeping in mind to round up the 3rd decimal place.

the choices are 1.600 and 1.604

 

[Ashleyz]

Wouldn't that give you x_0=2 , x_1 \approx 1.731, x_2 \approx 1.623 and x_3 \approx 1.605?

soo if you are asked to find x2...would that not be 1.623?

no. I think you are confusing x0 with x1. the order goes: x0
x1
x2
ect.