It might be appreciated that you help me to figure out answers and steps too..

I don't know where to start with.. so please give me detailed steps.

Question 1 Find the stationary points of the function f (x, y) = x3 + 3xy2 - 4y3 - 3x and determine their nature. (20 marks) Question 2 Compute the following multiple integrals using suitable methods. (a) ffp xy dxdy, where R is the region bounded by x-axis, y = 2x, and y = 4-2x. (15 marks) (b) July 716-x2-ya dxdydz, where V is the region bounded above by a sphere x2+y2 + z? = 16 and bounded below by a plane z = 1. (15 marks) Question 3 Let F(x,y,z) = cy i+ (x + z cosy) j + siny k, where c is a real constant. (a) Find the value of c such that F is irrotational. (5 marks) (b) With the value of c obtained in (a), determine a potential function @(x, y, z) such that Vo = F. (10 marks) (c) With the value of c obtained in (a), evaluate f. F . di, where C is the path moving from a point (0,0,0) to (1,n/2, n/2) along a straight line. (5 marks) Question 4 Compute the following integrals using suitable methods. (a) Jfs (x2 + y?)dS, where S is the part of the surface z = 9-2x-y lying inside the cylinder *+y=1. (15 marks) (b) ff, F . nidS, where F = xi + yj + z k and S is boundary surface of the region bounded by the cone z = 13(x2 + y?) and the upper half sphere x2+y2 + z? = 8 (here it is the outward-pointing normal). (15 marks)