Find the points on the boundary where f attains its

Question

Suppose that the temperature z over the plane is given by z = f(x,y), where f(x, y) = x²y - y³.

a. Show that the only critical point is at (0,0).

Use the factorization f(x,y) = y (x² - y²) to conclude that this point is a saddle point.

b. Now suppose that we are restricted to the unit disc x² + y²

1. Find the points on the boundary where f attains its absolute max and min. What is the absolute max and min of f?