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2220hw4answers - √ 7 2 0 Farthest point − √ 2 − √...

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Math 2220 Problem Set 4 — answers only Spring 2010 These answers are copied from the instructor’s solution manual, so I hope they are correct. Section 4.3 : 4. Critical point at (3 / 2 , 1). 8. Critical points ( 1 / 3 , 2 / 3 , (3 + 3) / 6) and (1 / 3 , 2 / 3 , (3 3) / 6). 18. Maximum of 9 3 at (3 3 , 3 3 , 3 3), minimum of 9 3 at ( 3 3 , 3 3 , 3 3). 20. Dimensions 18 × 18 × 36. 22. Radius 6 feet, height 21 feet. 26. (1 , 2 / 5 , 11 / 5). 32. Nearest points ((1+ 7) / 2 , (1 7) / 2 , 0) and ((1 7) / 2 , (1+ 7) / 2 , 0). Farthest point (
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Unformatted text preview: √ 7) / 2 , 0). Farthest point ( − √ 2 , − √ 2 , 2 + 4 √ 2). Section 2.6 : 40. (a) When both z n = 0 and y n = 0. (b) When both x n = 0 and y n = 0. (c) Everywhere except on the y-axis or the z-axis. 44. (a) All level sets are unions of smooth curves except the level set F ( x, y ) = 1. (b) All level sets are unions of smooth surfaces except the level set F ( x, y, z ) = 1. 1...
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