b) Let xy + xzin(yz) =1. Find Oz ax by using implicit function theorem. c) Determine the type of critical points of the function f(x,y) =x y +4xy -2y by using second derivative test. Question 4: July 2020 a) Let z = In(e* + y? ) , x =2t and y =+3 . Find az dt b) Let sin (x + y2 +2z) + x2 +z? =3 . Find oz Ox c) Find all the critical points for the function f(x, y) = x3 - xy + y and classify each of them as relative extrema or saddle point. Question 5: Jun 2019 a) Find and sketch the domain for f (x, y ) = In(x2 - y). b) Find oz and oz ox ay if ez - 2xz2 + sin(xy ) =10y defines z implicitly as a function of x and y c) Find all critical points of the function f (x, y ) =8y + x + 6xy and classify each as relative extrema or saddle points