Numerical Analysis

Code needs to be written in Python

$($a$)$ Implement in code the bisection method and use the code to solve the following problems up to

tolerance of $|f(x)|f$ tol $={10}^{-6}.$

$f(x)=[(\frac{}{x}{)}^{12}-2(\frac{}{x}{)}^6]$ with $=1$ on an interval $0\mathrm{.}5,10.$

Remark: function $2$ is called the Lennard$-$Jones potential and can be used to describe the energy

potential between two atoms or molecules. It is used in many chemistry, biology, and materials

science applications.

$($b$)$ For each function, predict the number of iterations required to achieve the given tolerance and compare

with the actual number of iterations your algorithm took. Analyze and explain the results.