Learning starts with a question. Asking is a signal for knowledge request!
First time here? Checkout the FAQs!

*Math Image Search only works best with SINGLE, zoomed in, well cropped images of math. No selfies and diagrams please :)

0 like 0 dislike
use Newton's Method to determine \(x_{2}\) for the given function and given value of \(x_{0}\).

\[f(x)=x^{3}-7 x^{2}+8 x-3, x_{0}=5\]
in Mathematics by Platinum (102k points) | 395 views

1 Answer

0 like 0 dislike
Best answer
Here is the derivative of the function since we'll need that.
f^{\prime}(x)=3 x^{2}-14 x+8
We just now need to run through the formula above twice.

The first iteration through the formula for \(x_{1}\) is,

The second iteration through the formula for \(x_{2}\) is,
So, the answer for this problem is \(x_{2}=5.71875\)
Although it was not asked for in the problem statement the actual root is \(5.68577952608963\). Note as well that this did require some computational aid to get and it not something that you can, in general, get by hand.
by Platinum (102k points)
Find the value of \(\dfrac{x^{3}+5 x^{2}+4 x+3}{x^{3}}\)

Related questions

2 like 0 dislike
1 answer
1 like 0 dislike
1 answer
2 like 0 dislike
1 answer

Join MathsGee Q&A, where you get instant answers to your questions from our AI, AstraNova and verified by human experts. We use a combination of generative AI and human experts to provide you the best solutions to your problems.

On the MathsGee Q&A, you can:

1. Get instant answer to your questions

2. Convert image to latex

3. AI-generated answers and insights

4. Get expert-verified answers

5. Vote on questions and answers

6. Tip your favorite community members

7. Join expert live video sessions (Paid/Free)

8. Earn points by participating

9. Take a course

10. Enjoy our interactive learning resources

Posting on the MathsGee Q&A

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines

MathsGee Q&A Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.

MathsGee Q&A


Social Proof

Web Analytics