In Problem use Theorem 2 to find the local extrema.

f(x, y) = x² + 3xy + 2y² + 5

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THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. f(a, b) = 0 and f,(a, b) = 0[(a, b) is a critical point] 3. All second-order partial derivatives of fexist in some circular region containing (a, b) as center. 4. A = fa (a, b), B = fy (a, b), C = fyy(a, b) Then 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 1. If AC - Case 4. If AC B2 0, the test fails.