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Chapter 4 144

# Chapter 4 144 - 406 27 28 29 3 CHAPTER 4 APPLICATIONS OF...

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Unformatted text preview: 406 27. 28. 29. 3 CHAPTER 4 APPLICATIONS OF DIFFERENTIATION y— — — —3: «2 + as A. D: [— 2. 00) B. y—intercept: f(0) : 0; ac—intercepts: —2 and 0 C. No . 1 3:3 —I— 4 symmetry D. No asymptote E. f’(m) = —\$— + \/2 + at = —— as + 2 2 + m = —— = 0 2v2+x 2\/2+m[ ( )] 2\/2+1: when a: : “3. so f is decreasing on (12__%) and increasing on (—§,oo). F. Local minimum value f(——) = —— if: —J£~ ~.—1 09 no local maximum H. 3’ 2\/2+w-3~(3m+4) v21+zc G’ film 2 4(2 + cs) _ 6(2+\$)— (3m+4) i 3m+8 _ 4(2 + 903/2 T 4(2 + ac)3/2 f”(a:) > 0 for a: > ~2. so f is CU 0n (—2, 00). No IP y : f(:v) = \/_ 7 {1/5 A. D : [0.00) B. y—intercept 0; w—intercepts 0. 1 C. No symmetry D. lim (ml/2 7 E”) : lim [ml/3 (531/6 — 1)] : 00., no asymptote , _ 3x1 6 — 2 E f(\$)=§ 1/2 :50 2/3:W>0 4:) 3m1/6>2 <1) :c>(§)6.sofisincreasingon ((§)6 :00)\$ and decreasing on (0. (96)}‘1 . .f()( ()§ 6): —— 7is a local minimum value _ , 8 9 1/6 G. f”(m) = fix 3/2 + gm 5/3 _——;6m§/3 > 0 41> 9.1/6 <3 <=> m < (3)6.sofis CU on (0, (g) ) and CD on (( IP at ((3)6 . 77%) y : f(w) : sin2m — 2cosm A. D : R B. y—intercept: f(0) : —2 C. f(—;v) : f(nc) so f is symmetric with respect to the y—axis. f has period 271’. D. No asymptote {DIOO rim). E. y' : 2sinmcosa: + 2sina: : 2sinm(cosm + 1). y' : 0 {i} sinac : 0 or cossc : —1 4:) av : mr or at : (2n + 1)7r. y’ > 0 when sina: > 0. Since cosm + 1 2 0 for all m. Therefore. 1/ > O (and so f is increasing) on (27m, (2n + 1)7r); y’ < 0 (and s0 f is decreasing) on ((2n — 1)7T, 27m). F. Local maximum values are f((2n + 1)7r) = 2; local minimum values are f(2n7r) : —2. G. 3/ : sin 29: + 2sinm :> y" :2cos29:+2cos;v : 2(2c0s2x — 1) +2cosa: : 4cos2zc+2coscc i 2 : 2(2cos2 5c +0081? — 1) : 2(2cosa: i 1)(cosa: + 1) N :0 <=> cosa: : % 0r—1 <:> m:2n7rzl:%ora:: (2n+1)7r. y" > 0(andsofisCU)0n (2mr — 1.272% + g); y” g 0 (and so f is CD) on (27m + g, 2mr + 5?“). There are inﬂection points a(t2n7ri — “El ...
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