Exam2_Sum07 - APPM 2350 Exam#2 Summer 2007 Be sure to...

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APPM 2350 Exam #2 Summer 2007 Be sure to include your name and a grading table on the front of your blue book. You must work all of the problems on this exam. Show ALL of your work and BOX IN YOUR FINAL ANSWERS . A correct answer with no relevant work may receive no credit, a wrong answer with no work will receive no credit, and an incorrect answer accompanied by some correct work may receive partial credit. Text books, class notes, crib sheets, cell phones, calculators, or electronic devices of any kind are NOT permitted. Please start each problem on a new page. Good luck! 1. (21 points) A large closed rectangular box sits in the first octant with three faces in the coordinate planes. The vertex of this box that does not touch any of the coordinate planes (the one out in space) intersects the plane x a + y b + z c = 1 where a , b , and c > 0. Find the position of the vertex that maximizes the volume of the box. 2. (20 points) Loedz is a very creative spider. He built an elaborate web one night in an inspired frenzy which can be modeled as the function x 2 + 3 yy 3 . His less creative
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