Question $4(25$ marks$)$

$($a$)$ Find the critical points of following function, then determine whether they are relativemaximum, relative minimum or saddle points.

$f(x,y)=2x^3-15x^2+36x+2y^3+15y^2-36y+12$

$[15$ Marks$]$

$($b$)$ Find the divergence and curl of the following vector fields:

i$.F(x,y,z)=$yzi$+3y^{2}zj+4z^{2}k$

$[5$ Marks$]$

ii$.F(x,y,z)=zsinyi+3xzj-cos5zk$

$[5$ Marks$]$