$(1)$ The function $f(x)=x^2$ has a minimum at $x^{**}=0.$ It is easy to check that $f^{\text{'}}(0)=0$ but that $f^{\text{'}\text{'}}(0)0.$ Use Newton's method to approximate this minimum. Save the number of iterations it takes, with the initial iteration counting as an iteration, in a variable named A$4.$ Save the final iteration in a variable named A$5.$

$(2)$ Repeat the process above with $f(x)=x^{500}.$ Save the number of iterations Newton's method took in A$6$ and save the final iteration in A$7.$

$(3)$ Repeat the process above with $f(x)=x^{1000}.$ Save the number of iterations Newton's method took in A$8$ and save the final iteration in A$9.($Your final iteration for this and the previous part may look strange, but you should be able to confirm that $f^{\text{'}}$ is very close to zero for these iterations.$)$