Use Newton$-$Raphson method to estimate the root of

Time left $0$:$19$:$00$

$f(x)=-3x^3+2x^2+5$

employing an initial guess of $x_0=2.$ Perform the computation for the first three iterations.

a$.1\mathrm{.}45472$

b$.1\mathrm{.}45449$

c$.1\mathrm{.}47113$

d$.1\mathrm{.}46789$