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Chapter 4 64 - —_—_—_—_—————— 326 43 44...

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Unformatted text preview: —_—__—_—__——————' 326 43. 44. 45. CHAPTER 4 APPLICATIONS OF DIFFERENTIATION y = f (:L') = 321nm A. D : (0. 00) B. w—intercept when Inns 2 0 4:) :L‘ = 1 . no y—intercept C. No symmetry D. liin $1113: 2 oo. I—’OO l 1 lim $1111 2 lim fl .5— lim /:c 2 lim (—x) :0. no H. 1_.o+ m—»0+ 1/x z_.0+ —1/x2 1—.0+ asymptote. E. f’ (m) : 11195 +1: 0 when Ina: : —1 <=> a: = 6—1. fl (cc) > 0 4:) 111m > —1 4:) a: > 6—1. so f is increasing on (1/6. 00) and decreasing on (01/6). F. f(1/e) = 71/6 is an absolute and local minimum value. G. f" (ac) : 1/$ > 0. so f is CU on (0. 00). No 1P $ IE y : f(:1:) : eI/zc A. D 2 {2: I w # O} B. No intercept C. No symmetry D. lim e_~ 2 lim §1_ : oo, gov—+00 a) m—mo lim — :0.soy:0isaHA. lirn —— : oo. lim — : —oo.soa::0isaVA. 1—>*00 I m—rO‘I’ 93 a:—>0— 113 It i E E. f’(x):%e_>o 4:» ($#1)ew>0 4:» m>1. so f is increasing on (1. 00). and decreasing on (700. 0) and (0.1) . F. f(1) : e is a local minimum value. G. f"($) 1 $2(£E€m) — 212(1163” 4 ex) : 61(332 — 2m + 2) > 0 I174 $3 <=> $>Osincem2r2x+2>Oforallzc.SofisCUon(0.oo)andCD on (goo,0). N0 IP y : f(:c) : me” A. D : R B. Intercepts are 0 C. No symmetry 1 . D. lim $6”: : lim 3:— ; lim —— :0.soy:015aHA. 2—400 12—»00 ea: m—wo 6"” lim are” : #00 E. f’(7:) : 6—3” — ace—C” : e_$(1 — m) > 0 4:) T—’*OO cc < 1. so f is increasing on (—00. 1) and decreasing on (1. 00). F. Absolute and local maximum value f (1) : 1/e. G. f”(:v) : 6”” (a: ! 2) > 0 <=> 30 > 2. so f is CU on (2.00) and CD on (#002). IP at (2.2/62) y:f(m) :1n(a;2 —3x+2) =1n[(:1:— 1)(a:—2)] A. D:{xinR:x2—3w+2>0} :(—oo.1)U(2.oo). B. y«intercept: f(()) z 1112; air—intercepts: f(a:) : 0 4:) m2 e 330 + 2 — e0 9 3:2 3:0 + 1 _ 0 3 22% => :6 m 0.38, 2.62 C. No symmetry D. lim f(a:) : 1113+ fix) : ~00. so m : 1 and I—fl' 1‘4 2 —3 295—32 a::2areVAs.NoHA. E. f’(m):$2—:33—m:mgysoffi)<0for$<1andf'(w)>0 1:: ...
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