Problem $4(20$ points$)$ Use Newton$-$Raphson method to determine a root of

$f(x)=x^5-16\mathrm{.}05x^4+88\mathrm{.}75x^3-192\mathrm{.}0375x^2+116\mathrm{.}35x+31\mathrm{.}6875$

Using an initial guess of $x=0\mathrm{.}5825$ and stopping criteria of $0\mathrm{.}01\%.$

IN MATLAB