Bisection and Newton's Approximation

[arhzz]

TL;DR Summary: Writing functions for Bisection and Newtons Approximation in Mathematica

Hello! I need to write 2 functions in mathematica, to find the roots of functions. The functions are the Bisection methods and Newtons Approximation.

(b1) Write your own function ApproxBisect[a0_,b0_,n_], which starting from an initial interval [a0, b0] approximates a root of the function in n steps. As a result, output the list of the n interval midpoints and the corresponding function values.

(b2) Test your function for the function f over a suitably chosen range and an appropriate number of approximation steps.

The function f(x) is this $f(x) = \sinh(x) - 2^x + x^4 - 2x^3 - 26x^2 + 4x + 48$

Now this is my attempt at the solution (since I dont know how to post mathematica code formatted nicely I will put a screenshot)

For Newton I tried this

And I printed all the values as a list (I can post a screenshot of the code if necesarry)

Now my main question is this ; Would you say this is correct ? I have never programmed in mathematica before so it is very new to me and I am not the most skilled programmer as it is. And since this is a team project I really dont want to be the reason we get a bad grade or worst case scenario fail the class.


Secondly, as I've stated that I am a beginner in mathematica, all tipps/tricks/suggestions are welcome; (efficiency,readability etc.) Also any good literature (crashcourse would be ideal) in mathematica is also appreciated.

Thanks in advance!

 

[scottdave]

For specifics on Mathematica, try here https://reference.wolfram.com/language/

If you are new to programming, try a flowchart or pseudocode first.

Test the behavior of your solutions on some polynomials that you know how to calculate the roots of.

For tips on entering programming code here, check out https://www.physicsforums.com/help/bb-codes

and scroll down to the programming section.