# HW09-solutions - perez(cp32376 HW09 hong(52960 This...

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perez (cp32376) – HW09 – hong – (52960) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Determine f x - f y when f ( x,y ) = 4 x 2 + 4 xy - 3 y 2 + x + 2 y. 1. f x - f y = 12 x - 2 y + 3 2. f x - f y = 12 x + 10 y + 3 3. f x - f y = 4 x + 10 y + 3 4. f x - f y = 12 x - 2 y - 1 f x = 0 , f y < 0 2. f x = 0 , f y > 0 3. f x > 0 , f y > 0 4. f x < 0 , f y = 0 5. f x < 0 , f y > 0 6. f x < 0 , f y < 0 7. f x > 0 , f y = 0 correct 8. f x = 0 , f y = 0 5. f x - f y = 4 x - 2 y - 1 6. f x - f y = 4 x + 10 y - 1 correct 002 10.0points Determine whether the partial derivatives f x , f y of f are positive, negative or zero at the point P on the graph of f shown in P x z y P f x > 0 , f y = 0 . keywords: surface, partial derivative, first or- der partial derivative, graphical interpreta- tion 003 10.0points Determine f x when f ( x,y ) = ( x 2 - y )(2 y 2 - x ) . 1. f x = 0 , f y < 0 2. f x = 0 , f y > 0 3. f x > 0 , f y > 0 4. f x < 0 , f y = 0 5. f x < 0 , f y > 0 6. f x < 0 , f y < 0 7. f x > 0 , f y = 0 correct 8. f x = 0 , f y = 0 From the graph it thus follows that at P f x > 0 , f y = 0 . keywords: surface, partial derivative, first or- der partial derivative, graphical interpreta- tion 003 10.0points Determine f x when f ( x,y ) = ( x 2 - y )(2 y 2 - x ) .