$f(x)=e^{{10}^{-50}x+{10}^{-51}}-{10}^{-1}x-1.($b$)$ For this sub$-$question $($Question $1($b$)),$ you are required to build MATLAB functions for each of the open

root finding methods we have discussed in this course: the Secant Method, Newton's Method, and the "Simple"

Fixed Point Method. Each MATLAB function should take as input a real$-$valued symbolic function $"f",$ an

initial guess for the root $"x0"($and an additional initial guess $"x1"$ in the case of the Secant Method$),$ a desired

number of significant digits $"$p$"$ to which the root approximation should converge, and a maximum number

of iterations "nmax". For each method, design your algorithm to iterate until either the approximation has

converged to $"$p$"$ significant digits or the number of iterations has reached "nmax".

For the same function $f$ considered in Question $1($a$)$:

i$.$ Use your Secant Method MATLAB function to approximate the roots of $f$ to $10$ significant digits. If there

are multiple roots, they should all be found by applying the Secant Method multiple times, adjusting the

initial guesses $"x0"$ and $"x1"$ as needed.

ii$.$ Use your Newton's Method MATLAB function to approximate the roots of $f$ to $10$ significant digits. If

there are multiple roots, they should be found by applying Newton's Method multiple times, adjusting

the initial guess $"x0"$ as needed.

iii. Attempt to use the "Simple" Fixed Point Method to approximate the roots of $f$ to $10$ significant figures.

If there are multiple roots, they should be found by applying the "Simple" Fixed Point Method multiple

times, adjusting the initial guess $"x0"$ as needed. Is it possible to make the "Simple" Fixed Point Method

work in order to approximate all the roots of $f?$ If not, explain when and how you were able to anticipate

the failure of this strategy.