Newton Iteration with Visualization

Please write the programs directly into the section programs at the end of this notebook!

The Problem

Write a program that computes the zero of a given function f using Newton's iteration starting from a given value s. You need not care about convergence, you can assume the iteration converges with the given f and s.
In addition to the approximated value of the zero, the program should produce a visualization of the iteration process, e.g. like in the following picture.

Your visualization need not look exactly the same, the picture above should only give an idea what it could look like. The picture should show the function, the tangents, the respective approximations to the solution after each step, the final solution, etc. Use colors and different line styles where appropriate.
You can choose which parameters your function should take, how they are structured, etc.

Programs

Test Examples