(15 pts)

For this problem, you’re going to use your initials to construct your own personal, monic cubic. A monic cubic is a cubic polynomial with leading coefficient equal to 1. Thus, it has the form

We just have to figure out what a, b, and c are going to be. Here’s how we’ll do it:

Let F, M, and L denote the positions in the alphabet of your First, Middle, and Last initials. If you happen to be missing your Middle initial, then let M=0. Then, let

Then,

- Use a LaTeX snippet to type out your personal, monic cubic.
- Use a LaTeX snippet to type out the Newton’s method iteration function for your personal, monic cubic.
- Perform two Newton steps from x_0=1 to find x_1=N(x_0) and x_2=N(x_1).
- Use software to graph your personal, monic cubic and include it in your post.
- Using the graph, find some good initial seed x_0 that is strictly larger than the largest real root of your personal, monic cubic and use Python to compute 10 Newton steps to approximate the root.