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211-bolotin-07spex02 - Math 211 A Spring.2007 Exam II s...

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Unformatted text preview: Math 211 , . , A Spring .2007 Exam II ' s. Bolotin Lecture 2 Your Name: Your TA: Your Section Meeting Time: Show all your work: no work - no credit. Leave your answers in exact forms (using 6, 1x12, x/i and similar numbers). Circle your answer. You. may use the last page as "scratch paper, but it will not be checked. Hand in your exam to your TA. Page 2 Math 211 — Exam II - Bolotin - 03/14/2007 V Page3 II. (20 points) The equation V 31:2 + y2 = Zez’y defines y as a function of 11:. Find the slope of the curve y = y(:z:) at the point Math 211 - Exam II - Bolotin ~ 03/14/2007 Page4 III. (20 points) Suppose f(:z:) = $4 — 83:3 + 1811:2 + 2. (a) What are the critical points of flan)? (b) What are the intervals on which f (2:) is increasing? Decreasing? (c) What are the intervals on which f (as) is concave up? Concave down? (d) Give all :1: values at which f(:c) has a local minimum. Math 211 - Exam II - Bolotin - 03/14/2007 Page 5 IV. (20 points) Suppose 3:2 + 4 f(m) —— $2 _~ 4' (a) Findrthe vertical and horizontal asymptotes. (b) Find the intervals on Which flat) is increasing (decreasing). (c) Find the intervals Where f (:15) is concave up (down). ((1) Sketch the graph y = f (cc) Math 211 - Exam II - Bolotin - 03/14/2007 Page 6 V. (20 points) A closed box with a square base is to have a volume of 250 cubic V feet. The material for the top and the bottom of the box costs $2 per square ' feet, and the material for the sides costs $1'per square feet. Find the minimal possible cost of the box. Math 211 - Exam II - Bolotin - 03/14/2007 Page7 Scratch paper ...
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