(a) Find the minimum and maximum values of the function
a: R² → R, a(x, y) = x²y.
subject to the constraint
x² + y = 1.
Also, at which points are these minimum and maximum values achieved?
(b) Which of the following surfaces are bounded?
S₁ = {(x, y, z) € R³ | x+y+z=1},
S₂ = {(x, y, z) € R³ | x² + y² + 2z² =4),
S3 = {(x, y, z) €R³ | x² + y²-22² =4).