Question 3 [25 marks].
(a) Find the minimum and maximum values of the function
g: \mathbb{R}^2 \to \mathbb{R}, \quad g(x, y) = x^2 + y^2,
subject to the constraint
x^4 + y^4 = 1.
Also, at which points are these minimum and maximum values achieved?
(b) Does the function
q: \mathbb{R}^2 \to \mathbb{R}, \quad q(x, y) = y
have a maximum value subject to the constraint
x + y = 0?
Explain why or why not.
