HW$2-$Q$3)$ MATLAB, PLEASE MAKE CODE COPYABLE

Newton$-$Raphson

Use the Newton$-$Raphson method to estimate the root after $7$ iterations for the function:

$g(x)=5x^2-0\mathrm{.}7x-33$

Use an initial guess of $x_0=0\mathrm{.}6.$

a$)$ Save the answer from each iteration in a vector. You must use a loop and your single line

calculation must be performed by accessing the proper element in the vector and assigning

the result to the proper element in the same vector. For example, suppose you call the

vector $x.$ Then the one line in the loop would be $x(?)=x(?)-.$ You will need

to determine what should replace the question mark and what should be inserted in the

blank.

So$,$ before the first iteration, you would have a vector $x=[x0],$ after the first iteration, $x$

$=\left[\begin{array}{cc}x0& x1\end{array}\right],$ and so forth

Display the vector as a column vector using the disp command. Make sure the values in

the vector are displayed in the long format. Make sure to change back to short afterwards!

b$)$ Calculate the exact real root using the roots function. Display using an fprintf

statement with $10$ digits to the right of the decimal point.

c$)$ In text, answer the question: "Why does the Newton$-$Raphson method initially overshoot

the exact value and then increase $($or decrease$)$ to converge to the exact value?"