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Chapter 3 12

# Chapter 3 12 - 162 CHAPTER 3 DIFFERENTlATlON RULES...

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Unformatted text preview: 162 CHAPTER 3 DIFFERENTlATlON RULES 2544:2336“ => y’=2(\$~ex+em-1)=20m(x+1).At(0,0).y’2260(0+1)=2~1-1=2iandan equation ofthe tangent line isy—0:2(m—0).ory:2x. _e: , mkeIier-l e“(a:—1) a: _> y _ m2 m2 y—e=0(a:—1).0ry=e. 1 26. y — . At (1. e). y’ = 0. and an equation of the tangent line is 27.(a)y=f(\$):1+ac2 : , __(1+-x%(0)—7M2x)_> _2x f (ac) # -———-———(1 +x2)2 ‘ (1 + :32)? So the slope of the tangent line at the point (—1.%) is f’(—1) = g 2 % and its equationisy~é—%(:c+1)ory:%x+1. _ m 11+m2 1+3v2 1—3: 21: 1— 2 ( ) 2( )2 a: 2.Sotheslopeofthe (1+2?) (1+:c2) tangent line at the point (3, 0,3) is f’(3) : {—053 and its equation is y — 0.3 : —0.08(m — 3) Dry 2 ~0.08:B + 0.54. 28- (a) y = f (i) => Ha?) e 3 \$3021) — e“6 32:2 \$26“ a: 7 3 €I(\$ — 3 29. (a)f(ac):— ;» f’(\$);[email protected]_3)2(_l:__(m6__):_;4_) f’ = 0 when f has a horizontal tangent line, f ' is negative when f is decreasing. and f' is positive when f is increasing. (:82 7 1)2 (\$2 — 1)2 Notice that the slopes of all tangents to f are negative and f’(a:) < 0 always. 31. We are given that f(5) : 1. f’(5) : 6. 9(5) : —3. and g’(5) = 2. (a) (f9)'(5) : f(5)9'(5) +9(5)f'(5) # (DO) I ( 3)(5) — 2 e 18 — —16 (b) ([y (5) Z 9(5)f'(5) — f(5)9'(5) _ (e3)(6) - (1X2) 2 #@ [51(5)]2 (—302 9 g I _ f(5)9'(5) '9(5)f'(5l : (1X2) - (—3)(6) I 2 (C) (f) (5) ’ mm]2 (1)2 0 ...
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