2.5 Class Notes

# 2.5 Class Notes - March 1 Lecture HWK#5 due R 3/8 or F 3/9...

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March 1 Lecture HWK #5 due R 3/8 or F 3/9 5.3: 36, 42, 50, 68 6.1: 14, 16, 43 6.2: 9, 18, 26 Spring Break March 17-25 Prelim 2: Thursday March 29 Prelim 2 changes Solutions will be available on the web after the exam is over. No questions will be answered during the exam All four TAs will be present March 1 Lecture A necessary condition to be an extremum (minumum or maximum) is f (c)=0 Second derivative test f ′′ (c) > 0 convex, minimum f ′′ (c) < 0 concave, maximum Problem 2 Where does the function ( ) 1 achieve its maximum for t > 0? t f t t = + Maximize f(t) = t / (1+t 2 ) 2 2 2 2 2 2 2 2 2 2 2 4 2 4 1(1 ) (2 ) 1 '( ) (1 ) (1 ) '(1) 0 2 (1 ) (1 ) 2(1 )(2 ) "( ) (1 ) 2(2) "(1) 0 maximum 2 t t t t f t t t f t t t t t f t t f + = = + + = + + = + = < Problem The energy E expended by a bird looking for food, depends on the amount of time F spent foraging for food. Find the time F that minimizes E if 2 2 0.25 E F F = +

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Minimize E = 0.25F + 2/F 2 3 3 1/3 4 1 '( ) 4 4 16 (16) ''( ) 12 0 minimum E F F F F E F F = = = = > Optimal can design Example 4 in 6.2. In manufacturing a cylindrical can the top and bottom costs 1.5 times as much as
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