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Homework9 - yp968 Homework 9 Radin(58415 This print-out...

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yp968 – Homework 9 – Radin – (58415) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points 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 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 8. f x = 0 , f y = 0 002 10.0 points Determine f x when f ( x, y ) = cos(3 y - x ) - x sin(3 y - x ) . 1. f x = - x cos(3 y - x ) 2. f x = - 2 sin(3 y - x ) - x cos(3 y - x ) 3. f x = x cos(3 y - x ) - sin(3 y - x ) 4. f x = x cos(3 y - x ) 5. f x = x sin(3 y - x ) 6. f x = - x sin(3 y - x ) 7. f x = 2 sin(3 y - x ) - x cos(3 y - x ) 8. f x = - cos(3 y - x ) - x sin(3 y - x ) 003 10.0 points Find the slope in the x -direction at the point P (0 , 2 , f (0 , 2)) on the graph of f when f ( x, y ) = 4(2 x + y ) e - xy . 1. slope = - 10 2. slope = - 6 3. slope = - 12 4. slope = - 8 5. slope = - 4 004 10.0 points Determine h = h ( x, y ) so that ∂f ∂x = h ( x, y ) (4 x 2 + 4 y 2 ) 2 when f ( x, y ) = 3 x 2 y 4 x 2 + 4 y 2 . 1. h ( x, y ) = 24 xy 2 2. h ( x, y ) = 24 x 3 y 3. h ( x, y ) = 12 x 3 y
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yp968 – Homework 9 – Radin – (58415) 2 4. h ( x, y ) = 12 xy 2 5. h ( x, y ) = 12 xy 3 6. h ( x, y ) = 24 xy 3 005 10.0 points Find f y when f ( x, y ) = integraldisplay x y cos ( t 7 ) dt .
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