Problem 30. Use Theorem 2 (below) to find the local extrema of f(x, y) = 2y36xy - x Theorem 2: If (1) z = f(x,y) (2) fr(a, b) = 0 and fy (a, b) = 0 (3) All second-order partial derivatives of f exist in some circular region containing (a, b) as center. (4) Afxx (a, b), B = fxy(a, b), C = fyy(a, b) Then Case 1. If AC - B2 > 0 and A < 0, then f(a, b) is a local maximum. Case 2. If AC- B2 > 0 and A > 0, then f(a, b) is a local minimum. Case 3. If AC- B2 < 0, then f has a saddle point at (a, b). Case 4. If AC-B2 = 0, the test fails.