Let $f(x,y,z)=x^3+y^3+z^3$ and $P_0=(1,2,3),$

$($a$)$ find the tangent plane of $f(x,y,z)=36$ at $P_0$;

$($b$)$ find the linearization of $f(x,y,z)$ at $P_0$;

$($c$)$ estimate the number $f(1\mathrm{.}07,1\mathrm{.}93,2\mathrm{.}93).$