The polynomial $f(x)=0\mathrm{.}00074x^4-0\mathrm{.}284x^3+3\mathrm{.}355x^2-12\mathrm{.}183x+5$ has a real root between $15$ and $20.$ Apply Newton$-$Raphson method to this function using an initial guess of $x_0=16\mathrm{.}15.$ Explain your results.

$\backslash$table$[[$Iteration$,x_i,f(x_i),f^{\text{'}}(x_r),|{}_a|$