How do I solve this?

1) Find the extrema subject to the stated constraints a) (Ex. 3.4.4, 4pts) f(x, y) = x - y subject to x2 - y? = 2 b) (Ex. 3.4.6 4pts) f(x, y, z) = x + y + z subject to x2 - y? = 1 and 2x + z = 1 2) (Ex. 3.4.12, 6pts) Use the method of Lagrange multipliers to find the absolute maxi- mum and minimum values of f(x, y) = x2 +y2 - x - y + 1 on the unit disc. 3) (Ex. 3.4.20 6pts) A rectangular box with no top is to have a surface area of 16m. Find the dimensions that maximize its volume. 4) (Ex. 3.5.7 6pts) Show that x322 - 23yr = 0 is solvable for z as a function of (r, y) near (1, 1, 1) but not near (0, 0, 0). Compute Oz/Or and Oz/dy at (1, 1). 5) (Ex. 3.5.18, 6pts) Is it possible to solve the system of equations xy? + xzu + yo? = 3 u yz + 2.cv - u2v2 = 2 for u(x, y, z), v(x, y, z) near (x, y, z) = (1, 1, 1), (u, v) = (1, 1)? Compute dv/dy at (x, y, z) = (1, 1, 1)