Write a MATLAB script $10$ find all the roots of the following equation using the Secant Method.

$f(x)=x^3-3x^2+3$

This equation has three roots. Use the initial guess solutions in a $32$ array as shown below:

Root $1$:$-1$ and $0$

Root $2$:$1$ and $2$

Root $3$:$2\mathrm{.}2$ and $3$

The initial guess values should be stored in an array as instruted in the template.

Use a tolerance of ${10}^{-5},$ and $500$ maximum iterations.

You will use a for$-$loop. The number of steps in the for$-$loop should be equal to the number of roots.

Hint: A while$-$loop will be nested inside the for$-$loop to compute all the roots. After each root is computed, its value will be stored in an element of an array called Eqn Roo.

You should define a total of tive anonymous functions.

For reference about finding roots of equations using the Secant Method, refer to slides $22-29$ of Module$\_02.$ Note: We are not making a function file in this exercise.

The intormation about for$-$loop and while$-$loop were covered in Module$\_01$A$.$

Script $o.$

$\%$ Here, write your script for the problem statemenet above. Your script MUST be properly and completely commented to receive full credit.

$\%$ Define variables and functions as instructed below.

$\%$ NOTE: The complete instructions for this assignment was explained during the lecture in class.

$\%$ The anonymous function for f$($x$)$ must be named: F

$\%$ Define an$\text{'}$ anonymous function for the first derivative of f$($x$),$ called dF$.$ This anonymous function takes two inputs x$0,$ and x$1$ to perform numerical

differentiation, df$/$dx$,$ as explained in class.

$\%$ The anonymous function for g$($x$)$ must be named G$.$ This function takes two inputs x$0$ and x$1,$ and is used in the script to compute a new value based

$\%$ on our initial guesses. x$0$ and x$1$ are the guess solutions that the function uses to calculate a possible solution within the loop.

$\%$ The anonymous function for dg$/$dx must be called dG$.$ This takes three inputs x$0,$ x$1,$ x$2,$ and is used for convergence test. The equation for this

$\%$ anonymous function is the numerical differentiation of g

$\%$ Store the initial solution in an array variable named ini$\_$sol.

$\%$ The variable for the maximum number of iterations must be called max$\_$itr.

$\%$ You will have to store the roots of the equation in an array called Eqn$\_$Roo.

$\%$ Use a variable called iter to count your iterations inside the loop.

$\%$ Use a variable called Tol to determine the tolerance for the calculations.

$\%$ Inside the loop, you can use variables r$0$ and r$1$ to extract the first and second guesses for each root.

$\%$ You can use a variable called r$2$ to store the output of the function g

$\%$s After the solution is completed, print out the roots using the fprintf command in the following format:

$\%$ Root $1\mathrm{.}0$:$\{$tab$\}12\mathrm{.}3456\{$next line$\}$

& Note that MATLAB is case$-$sensitive$.$ Variables MUST be defined as instructed above, or points will be deducted.

$$8$ For this exercise, you need a for$-$loop and a while$-$loop nested in each other.