What is the absolute max and min of function

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Reference no: EM13968005

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?

Reference no: EM13968005

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