Find a root of the following function using hand calculations $($Not a MATLAB function or script$)$ by

a$)$ using the Newton$-$Raphson method with the initial guess of $x_0=-3,$ and

b$)$ using the Simple Fixed$-$Point method with the initial guess of $x_0=5\mathrm{.}1.$

c$)f(x)=x^5-11\mathrm{.}9x^4+43\mathrm{.}78x^3-41\mathrm{.}3x^2-44\mathrm{.}78x+53\mathrm{.}2$

For each method, perform the computations until ${}_a$ is less than $1\%.$ Also check your final answer. Most of the work should be done by hand calculations $($you can use MATLAB only as a calculator for this problem$).$