3. (a) (6 points) Expand S(x, y, z) around (20,40, zo) to the second order in…

3. (a) (6 points) Expand S(x, y, z) around (20,40, zo) to the second order in Az = 1 – TO, Ay=y – Yo, and Az = 2-20. Detailed derivation is required. (b) (3 points) Find the extremum of f(x, y, z) = xyz subject to the constraint g(x, y, z) = I+y+z-e= 0, where x, y, z are positive variables and c is a positive constant. (c) (6 points) Show explicitly the nature of the extremum found in (b).