122test2 - Find the relative extreme values of the...

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October 20, 2011 Math 122 - Test 2 Name__________________ Show work for full credit. For each function, evaluate the given expression. 1. a. f x y x y ( , ) ! ! ! 99 2 2 , find f ( , ) ! ! 3 9 b. f x y z z x y ( , , ) ln ! , find f e ( , , ) 4 1 ! For each function, find the partial derivatives, f x y x ( , ) and f x y y ( , ) . 2. f x y x y ( , ) ( ) ! + ! 2 1 3. f x y ye xy ( , ) ! 2 Find the second-order partials, f xx , f xy , f yx , and f yy . 4. f x y x x y y ( , ) ! ! + 3 2 3 2 5
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October 20, 2011 Math 122 - Test 2 page 2 of 3 5. Find the total differential, df , of the function f x y y x ( , ) ! . 6. Given the function f x y ye x x ( , ) ! + ! 2 , and values x ! 0, " x dx ! ! .1, and y ! 1, " y dy ! ! .05. Find df using differentials. (Do not use a calculator.)
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Unformatted text preview: Find the relative extreme values of the function. 7. f x y x y xy x y ( , ) ! ! ! + + + ! 2 2 2 4 5 2 2 October 20, 2011 Math 122 - Test 2 page 3 of 3 8. Use Lagrange multipliers to find the minimum value of f x y x y xy ( , ) ! + ! 2 2 2 subject to the constraint x y + ! 24. 9. Evaluate 3 8 # $ % # $ % xydxdy y . 10. The temperature x miles east and y miles north of a weather station is given by the function f x y x y ( , ) ! ! + 60 4 6 . Find the average temperature over the region below. 2 3...
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122test2 - Find the relative extreme values of the...

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