Q10 - Version 163 DGQ10 gilbert (55485) 1 This print-out...

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Unformatted text preview: Version 163 DGQ10 gilbert (55485) 1 This print-out should have 3 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Which one of the following properties does the function f ( x, y ) = x 3 + 2 xy 2 20 x 16 y + 22 have? 1. saddle point at (2 , 2) 2. saddle point at ( 2 , 2) 3. local max value 26 at ( 2 , 2) 4. local max value 26 at (2 , 2) 5. local min value 26 at ( 2 , 2) 6. local min value 26 at (2 , 2) correct Explanation: First we have to locate and classify the critical points of f . Now after differentiation, f x = 3 x 2 + 2 y 2 20 , f y = 4 xy 16 . Thus the critical points of f are the solutions of the equations ( ) 3 x 2 + 2 y 2 = 20 , xy = 4 . One solution of ( ) is (2 , 2), while (2 , 2) is not a solution, so we can concentrate on the critical point (2 , 2). But after differentiating once again, we see that f xx = 6 x, f yy = 4 x,...
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Q10 - Version 163 DGQ10 gilbert (55485) 1 This print-out...

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