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Unformatted text preview: Second Partials Test Let f have continuous second partial derivatives on an open region containing a point ( a,b ) for which ) , ( = b a f x and ) , ( = b a f y . To test for relative extrema of f, consider the quantity [ ] 2 ) , ( ) , ( ) , ( b a f b a f b a f d xy yy xx= . 1) If d > 0 and ) , ( b a f xx , then f has a relative minimum at ( a,b ). 2) If d > 0 and ) , ( < b a f xx , then f has a relative maximum at ( a,b ). 3) If d < 0, then ( a, b, f (a,b) ) is a saddle point . 4) The test is inconclusive if d = 0. #10 #25 #54 Section 12.9 #6 #20...
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 Spring '12
 PamelaSatterfield
 Calculus, Critical Point, Relative Extrema Occur

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