# Practice test 3-with-answers - Version 001 Practice test 3...

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Version 001 – Practice test 3 – karakurt – (1101103) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. CalC15g19a 001(part1of2)0.0points When f is the function defined for x, y > 0 by f ( x, y ) = ln( xy ) + 6 x 2 - 3 x - xy + 2 , locate its critical point. 1. critical point at parenleftBig 1 4 , 4 parenrightBig correct 2. critical point at parenleftBig 4 , 1 parenrightBig 3. critical point at parenleftBig 1 4 , 1 parenrightBig 4. critical point at parenleftBig 1 , 1 4 parenrightBig 5. critical point at parenleftBig 1 , 4 parenrightBig 002(part2of2)0.0points Which of the following statements most ac- curately describes f at this critical point? 1. local minimum value of 13 8 2. local maximum value of 5 8 3. local minimum value of 5 8 4. local maximum value of 13 8 5. saddle-point correct CalC15h33s 003 0.0points Use Lagrange multipliers to find the volume of the largest rectangular box in the first oc- tant with three faces in the coordinate planes and one vertex in the plane 3 x + 2 y + z = 9 . 1. volume = 3 2 2. volume = 9 3. volume = 9 4 4. volume = 27 2 5. volume = 9 2 correct CalC16b20a 004 0.0points Find the average value, I , of the function f ( x, y ) = 6( x + y ) ln x over the rectangle A = { ( x, y ) : 1 x 3 , 0 y 3 } .