Problem $1$: Write a MATLAB script called hw$4\_$p$1.$m to use Newton's method of optimization to

find the minimum of the function $f(x)=x^2-1.$ Use as the stopping

criterion. Use a starting guess of $\sqrt[\phantom{2}]{{}^{-1}}.$ Then run the script again with a starting

guess of $9,000\mathrm{.}1.$ Finally, run it again with a starting guess of your own choosing $($not

the minimum, though ${?}^3).$

In the same script, solve the problem using the Newton$-$Raphson method.

Discuss your results: Why did the algorithms work the way they did?

Note: This is an optimization problem$-$you need to think critically ${?}^4$ about how you

can use the Newton$-$Raphson method $($a root$-$finding method$)$ to solve an optimization

problem. Do not assume you know the minimum value.