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Chapter 4 147 - CHAPTER 4 REVIEW 409 36 m 2 ii =...

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Unformatted text preview: CHAPTER 4 REVIEW 409 36. m) 2 ii = acl/sfl—IEVl i —2/3 2 f’(a;)_m1/3( 1)(1 2:)—"’( 1) : (1 w)‘l(%)w‘2/3=m3 fits); ,, 90—2/3 (ac—1)2(2)—(1+2x)(2)(96—1) 1+2m 41—5/3 :_2x’5/35_w2fl f (IE) 7 3 (£13 _1)4 ($ _1)2< 9 > 9 (1' * 1)3 From the graphs. it appears that f is increasing on (A050. 1) and (1, 00). with a vertical asymptote at m : 1. and decreasing on (700., —0.50); f has no local maximum, but a local minimum of about f(70.50) = 70.53; f is CU on (71.17. 0) and (0.17, 1) and CD on (—00, —1.17). (0. 0,17) and (1, 00); and f has inflection points at about (—1.17,—0.49). (0. 0) and (0.17, 0.67). Note also that lim f(:c) :E—izizoo : 0. so y : 0 is a horizontal asymptote. 37. my) *3w6 5$5 : 304 5:123 21:2 i 2 ? f’(:c):18905 ~25x4+4$3 —15gp2 —4m :> f”(x) 4902;4 100953 1 1231:2 30m 4 ,045 —— 05 f’ fl 1" 2 —50 -4 From the graphs of f’ and f”, it 100 2 .5 appears that f is increasing on - (70.23. 0) and (1.62. 00) and decreasing on (—00. —0.23) and (0.1.62); f has a local maximum of 71,5 _‘. 15 _0,5 045 08 about f (0) : 2 and local minima of about f(70.23) : 1.96 and f(1.62) : —19.2; f is CU on (—00, —0.12) and (1.24., 00) and CD on (—0.12, 1.24); and f has inflection points at about (—0.12. 1.98) and (1.24. ~12.1). ...
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