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  3. In Problem use Theorem 2 to find the local extrema.f(x, y) =

In Problem use Theorem 2 to find the local extrema.f(x, y) =

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In Problem use Theorem 2 to find the local extrema.

f(x, y) = x2 + 8x + y2 + 25

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THEOREM 2 Second-Derivative 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 second-order 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

College Mathematics For Business Economics, Life Sciences, And Social Sciences

14th Edition

Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker

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