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Chapter 4 132 - 394 U CHAPTER4 APPLICATIONS OF...

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Unformatted text preview: 394 U CHAPTER4 APPLICATIONS OF DIFFERENT‘ATION 2 <$ S3is—1.sowegetto(3.1). f(3) :1 => —3+E=1 2 E:4.Thus, 2m~1 ifOngl f(:v)= a: if1<m<2 —x+4 if2gxg3 Note that f’(:1:) does not exist at a: : 1 or at ac = 2. 3 50. (a) (b) Since F(0) : 1. we can start our graph at (0., 1). f has a minimum at about in : 0.5. so its derivative is zero there. f is decreasing on (07 0.5), so its A derivative is negative and hence. F is CD on (0, 0.5) and has an IP at 71 4 :c m 0.5. On (0.5. 2.2). f is negative and increasing (f’ is positive), so F is '7‘ decreasing and CU. On (2.2. 00). f is positive and increasing. so F is 2 increasing and CU. (C) f(:c) : 2:17 * 3J5 :> (d) Fm) :12A3ém3/2—i—C. F(0) :Cand F(0):1 => 0:1.50 F($)=a:272m3/2+1. 1.1 ...
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