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Chapter 4 57

# Chapter 4 57 - SECTION 4.5 SUMMARY OF CURVE SKETCHING 319...

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Unformatted text preview: SECTION 4.5 SUMMARY OF CURVE SKETCHING 319 24. y : f(x) = an/Z — x2 A. D = [—x/i W] B. y—intercept: f(0) = 0; z—intercepts: f(\$) : 0 => m = 0, :l:\/§. C. f(—x.) 2 —f(ac). so f is odd; the graph is symmetric about the origin. D. No asymptote —m im2+2w\$2 2(1+:c)(1—m) E. ’ = -— v2~ 2— — . ’x isneativefor f“) 3” m+ ”5 m m f“ g —\/§ < x < ~1 and 1 < :c < ﬂ and positive for —1 < a: < 1. sof is decreasing on (—x/i ~1) and (1. ﬂ) and increasing on (—1.1). F. Local minimum value f(—1) = —1. local maximum value f(1) = 1. 2 r2( 4m) (2 2362) ”3 ,/ _ V2 ~ x2 G. f (ll?) — [(2—m2)1/2]2 (2 — x2)(—4ac) —l— (2 i 2x2):z: (2 D m2)3/2 _ 2953 — 6m a 2m? , 3) 7 (2 _ m2)3/2 * (2 ﬂ C(32)3/2 Sincezz:2 ~3 < Oforatin [~\/§\/§] f"(m) > 0for ~\/§< x < Dand f”(:z) < 0for0 < a: < x/i. Thus.fis CU 0n (—ﬁ. 0) and CD on (0, ﬂ). The only IP is (0, 0). 25. y=f(m):\/1~:c2/w A. D: {as lasl S 1., w 7% 0} = [~1. 0) U (0. 1] B. m—intercepts i1. no y~intercept V/ _ . 2 / _ 2 C. f(—\$) : —f(\$). so the curve is symmetric about (0, 0). D. lim ¥ : ()0. lim —1—\$ 2 —oo. z—»O+ 1) 24>0‘ :I.’ 2 4 ~ax/x/1—ac2 ~x/1—x2 1 \$03: : 0 is aVA. E. f’(x) — ( \$2) — 2W < 0. so f is decreasing on (~10) m —:c and (0. 1). F. No extreme values G. f”(x) : (1/31)) and (\$011321: (: §.i%) 26. y : f(av) : x/m A. D : (~oo.—1)U(1.oo) B. No intercepts C. f(—a:) : —f(ac). sof is odd; 0.7 the graph is symmetric about the origin. D. lim L 2 1 and lim 3: x—voo m 1—,,00 W : *1. so y = :1 are HA. lim f(m) : +00 and lim f(\$) : 700. so a: : :1 are VA. 2—>1+ 1—>71‘ I a m H i\$ — —1' _ — . \ .- E. f(£ll)— [(m2_1)1/2]2 —W—W<O.sofisdecredsmg ...
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