Understanding Newton's approximation method with an example

Question

Let $f(x)=x^2+3x-10$. If we take $x_0=0$ as the starting point for the Newton method, then the value of $x_2$ is what?

I have tried but it appears I am wrong somewhere as the exercise from where I have taken this problem does not matches my answer of -190/33.

Please take note of my edit and consider using MathJAX in the future... — abiessu, Sep 01 '21 at 05:04
How do you know you are wrong? Do you have the answer listed for you somewhere? — abiessu, Sep 01 '21 at 05:05
@abiessu There are multiple options to select from, none of which matches the above. — Splendid Digital Solutions, Sep 01 '21 at 05:06
Your work looks good, it is possible the problem is written incorrectly or may have been adjusted without correcting the set of answers... — abiessu, Sep 01 '21 at 05:25
@abiessu There has been a mistake in the calculation as pointed in the answer. Thanks for assuring me that the approach is okay. — Splendid Digital Solutions, Sep 01 '21 at 05:39

Robert Lee · Answer 1 · 2021-09-01T05:39:51.723

2

You have an error in your calculation for $x_1$. You should have $$ x_1 = 0 - \frac{f(0)}{f'(0)} = 0 - \frac{(0)^2 + 3(0) - 10}{2(0) + 3} = -\left(- \frac{10}{3} \right)=\color{red}{+} \frac{10}{3} $$ With this correction you should get $x_2 = \frac{190}{87} \approx 2.1839$, where you are indeed approximating the root $x=2$ of $x^2 + 3x -10$.

edited Sep 01 '21 at 05:39

answered Sep 01 '21 at 05:33

Robert Lee

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Understanding Newton's approximation method with an example

1 Answers1