In Problem use Theorem 2 to find the local extrema. f(x, y) = x 2 + 8x
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In Problem use Theorem 2 to find the local extrema.
f(x, y) = x^{2} + 8x + y^{2} + 25
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THEOREM 2 SecondDerivative Test for Local Extrema If 1. z = f(x, y) 2. fx(a, b) = 0 and f(a, b) = 0 [(a, b) is a critical point] 3. All secondorder partial derivatives of fexist in some circular region containing (a, b) as center. 4. A = f(a, b), B = fxy(a, b), C = fyy(a, b) Then Case 1. If AC   Case 2. If AC  B² > 0 and A < 0, then f(a, b) is a local maximum. B² 0 and A > 0, then f(a, b) is a local minimum. B² < 0, then fhas a saddle point at (a, b). Case 3. If AC = Case 4. If AC  B² = 0, the test fails.
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College Mathematics For Business Economics, Life Sciences, And Social Sciences
ISBN: 9780134674148
14th Edition
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker
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