# Q10 - Version 163 – DGQ10 – gilbert –(55485 1 This...

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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...

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