Mathematics 241 – Multivariable Calculus Quiz 7 – November 12, 2010

Your Name:

Let f(x, y) = sin(x) − sin(y).

A) (10) f has a critical point at (x, y) = (π/4, π/4). Classify it as a local maximum, local minimum, or a saddle point using the Second Derivative Test.

B) (10) Find the maximum and minimum values of f(x, y) = 6x^{2} + y^{2} on the constraint set S = {(x, y) | x^{2} + y^{2} = 1}. (Any correct method is OK.)