2.6 Class Notes - March 6 Lecture HWK #6 due R 3/15 or F...

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March 6 Lecture HWK #6 due R 3/15 or F 3/16 7.1: 10, 16, 24, 33, 36, 39 7.2: 10, 14, 18, 24, 32, 34 Spring Break March 17-25 Prelim 2: Thursday March 29 Covers up to and including 7.2. Problem A farmer wants to build pens to hold four animals. What is the maximum area that can be enclosed with 80 feet of fence? x yyyy Solution 2 5 8 80 (80 5 ) /8 () 4 ( 8 0 5 ) /2 '( ) (80 10 ) / 2 0 when 8 (80 40) / maxi 85 ''( ) 10 / 2 0 mum xy y x Ax x x x += = == =− = = < Word Problem A dog is sitting on a beach and sees Britney Spears in the water 80 meters from shore. The dog is a meters down the beach and can run 3 times as fast on the beach as it can swim through the water. What is the optimal path to save BS? a-x x 80 (80 2 +x 2 ) 1/2 Solution 22 1 / 2 1 / 2 1 / 2 2 Minimize ( ) (80 ) 3 (1/ 3) (1/ 2)(80 ) (2 ) 0 when (80 ) 3 80 9 800 28.28 ax fx x x x xx x =+ + + + = = =
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Second derivative 22 1 / 2 1 / 2 1 / 2 1 / 2 2 2 3 / 2 1 / 2 1 '( ) 3( 8 0 ) (80 ) (1/ 2)(80 ) (2 ) ''( ) (80 ) multiply top and bottom by (80 ) (80 ) 80 0 (80 ) (80 ) f convex: decreasing minimum then x fx x xx x x x x =− + + +− + = + + == > ++ ↓↑ increasing Time f(x) when a = 100 100-x = distance run along the beach 105 110 115 120 125 130 0 2 04 06 08 01 0 0 Minimum does not depend on a!
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).

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2.6 Class Notes - March 6 Lecture HWK #6 due R 3/15 or F...

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