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Chapter 4 66

# Chapter 4 66 - 328 49 50 CHAPTER 4 APPLICATIONS OF...

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Unformatted text preview: 328 49. 50. CHAPTER 4 APPLICATIONS OF DIFFERENTIATION F. Local maximum value f(e_2) 2 48”, local minimum value f(1) = 0 G. f"(m) = 2(1nz)(1/m)+ 2/m : (2/x)(lna: + 1): 0 whenlnm:—1 (I) m=e_1. f"(w)>0 4:} a: > l/e. sofis CU on (1/6. oo).CD on (0. 1/6). lPat(1/e,1/e) y : f(\$) : me A. D : R B. Intercepts are 0 C. f(73:) : —f(a:). so the curve is symmetric . . u — 2 . . about the ongm. D. 11m :36 a” : 11m \$9 2 11m 1 arr—>200 z—vioo ei“ ma::oo 211:5“: 2 :0.soy:0isaHA. 2 2 E. f’(m) : 6—1 — hie—z : 6-12 (1 a 23:2) > 0 <=> m2 < g 4i} [:6] < 7— so f1s1ncreas1ngon (#35. i) and decreasing on (#00, —%) and ),(% oo) . F. Local maximum value f<— 2—) — 1/’\/26 local minimum value f(!71=): —1/\/—; G. f"(n: — —231ce’\$2 (1 — 2352) — lime—“”2 : 2:ce””‘2 (25c2 * 3) > 0 4:} 10>ﬁor—ﬁ<z<0.sofisCUon()\/§,oo) H. and (#ﬁﬂ) andCDon (—oo.*\/:) and (0 ﬂ). 1P are (0. 0) and (:ﬁ iﬁe'm). y : f(a:) 2 ex # 36—?” — 4a: A. D : R B. y-intercept : #2; m—intercept % 2.22 C. No symmetry D. lim (eac -3e_\$ —4ac) : lim \$<e— —3e —4) :00. since lim 6— 2 lim 67 :00. 93800 (Ir—>00 .12 (I: \$—>()O :13 z->oo Similarly lim (6 e 3e" — 41:) : 700. No HA; no VA \$—>-oo E. f’(a:):e””+3€’m‘4:e_\$(621—4e\$+3):e_1(eI—3)(eI—1)>0 (I) ez>30re\$<1 4:) at > ln3 or m < 0. So f is increasing on (700, 0) and (1H3, 00) and H. y decreasing on (0.1m 3) . F. Local maximum value f (0) : —2. local minimum value f(ln 3) : 2 i 4 ln3 0 X 72 G. f”(a:) : ex -3e’1 : e_z(e2\$ -3) > 0 4:) 629” > 3 4:) x> 51113. sofisCU on(§1n3,oo) andCDon (—00.5113). IP at (g 1113. -21n3). ...
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