Question

Use Newton’s method to find a 6-decimal place approximation to the positive root of f(x) = x 5 − 7x 2 + 4 that is nearest to the origin.

(a) Tell your “Newton function” R(x)

(b) Tell what technology you used. (“Handheld calculator” is not acceptable.)

(c) Tell your initial guess (x1) and the iterations that you observed.

(d) Tell your “stopping criteria.” That is, why did you stop after n iterations

Answer 1

Solution:

Given function:

I have used Mathematica software on my personal laptop.

Initial guess:

Number of iterations: 3

Stopping criteria:

I used: .
Positive root: 0.783296,

correct to 6 decimal places.

Here is the code and the outputs:

If you have any doubt, please post your comment. Thank you.