TASK $1$:$(8-12$min$)$

Main Script $-$ Obtain and validate a user input for a coefficient vector

Prompt the user to enter a vector that contains the coefficients for a$,$polynomial.

Perform data validation to check that the user$-$entered vector contains an even number of elements

& HINT: Explore the rem$()$ or mod$()$ functions to help you. What is the remainder of an even number after dividing by $2?$ What is the remainder of an odd number after dividing by $2?$

Continue re$-$prompting the user to re$-$enter the vector until a valid entry is obtained. Limit the total number of tries to $5$ attempts.

If after the $5^{th}$ attempt, an invalid vector is still entered, display a warning, and remove the last entry so that you have an even number of elements in the vector:

Example: Invalid $=\left[\begin{array}{ccccc}1& 2& 3& 4& 5\end{array}\right]$ Valid $=\left[\begin{array}{cccc}1& 2& 3& 4\end{array}\right]$

Save the final vector as MA$3\_$Polynomial.csy

TASK $2$: $(5-10$min$)$

Main Script $-$ Obtain and validate a user input for the root value initial guess; obtain a percent error value

Review the help documentation for the polyval$()$ and polyder$()$ functions. Practice in the command window to make sure you understand how each of these functions works and what the outputs mean! This is essential for the rest of the MA$!$

Prompt the user to input an initial guess for $V_0{V}_v$ is the $x-$value at which the user$-$entered polynomial function entered in Task $1$ crosses the $x-$axis.

Perform data validation to check that the derivative of the polynomial does not equal zero at the user$-$entered $x$ value. You are checking that $T^{\text{'}}(V_0)0).$ Continue prompting the user to re$-$enter an initial guess until a valid entry is obtained. Limit the total number of tries to $3$ attempts.

diamond HINT: You will need to use polyval$()$ and polyder$()$

After three failed attempts to enter an $x-$value where the derivative does not equal zero, issue an error and terminate the program.

If a valid $x-$value is obtained, prompt the user to enter a percent error that will be used for the Newton$-$Raphson calculation. No additional validation on the percent error is required.

TASK $3$: $(15-25$min$)$

Function $-$ Calculate the true $x-$value where the function crosses the $x-$axis using the Newton$-$Raphson method Create a new function named FindZero,m

diamond Inputs: $(3)$ Final vector of coefficients from Task $1,$ initial guess for $V_a$ from Task $2,$ percent error from Task $2$ as a whole number.

diamond Outputs $(2)$ Final value for $V_6$ and number of iterations for the Newton$-$Raphson method

Within your function, repeatedly apply the Newton$-$Raphson method until the percent error between two subsequent iterations is less than the user$-$entered percent error.

Hint! polyval$()$ and polyder$()$ are very useful here!

Percent Diff $\frac{?}{a}=bs(\frac{\text{O}\text{u}\text{t}\text{p}\text{u}\text{t}-\text{P}\text{r}\text{e}\text{v}\text{i}\text{o}\text{u}\text{s}\text{O}\text{u}\text{t}\text{p}\text{u}\text{t}}{\text{P}\text{r}\text{e}\text{v}\text{i}\text{o}\text{u}\text{s}\text{O}\text{u}\text{t}\text{p}\text{u}\text{t}})*100$

If at any time the denominator in the Newton$-$Raphson calculation is equal to $0($i$.$e$,f^{\text{'}}(guess)=0),$ issue an error and terminate the program.