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Chapter 3 4 - 154 CHAPTER 3 DIFFERENTIATION RULES 39 y = $4...

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Unformatted text preview: 154 CHAPTER 3 DIFFERENTIATION RULES 39. y = $4 + 26m :> y' = 43:3 + 261. At (0, 2), y' = 2 and an equation of the tangent line is y — 2 : 2(cc — 0) or y = 2m + 2. 40. y : (1 + 2:10)2 : 1 + 41: + 4m2 : y’ = 4 + 81:. At (1, 9), y’ : 12 and an equation of the tangent line is y—9:12(x—1)ory:123:—3. 41.y:3a:2—:c3 : y'=6m*3$2.At(1,2).y’=6i323. 5 so an equation of the tangent line is y — 2 = 3(1: — 1). or y : 3m 7 1. (-71-. —1 42,1”,:;c\/g;:ag3/2 => y':gm1/2.At(4,8). 12 y’ = 3(2) : 37 so an equation of the tangent line is y-8:3($—4)7ory:3a:—4. 43. (a) 50 (b) —10 From the graph in part (a). it appears that f ’ is zero at 2:1 m —1.25. 1:2 z 0.5. and :33 m 3. The slopes are negative (so f’ is negative) on (—00, m1) and (3:27 3:3). The slopes are positive (so 1“ is positive) on (3:1, m2) and (:33, 00). (c) f($) : 2:4 — 3:33 — 6:122 + 7x + 30 :> 100 f'(a:) : 4x3 — 9:02 — 12:16 + 7 1-» 5 ‘3 "fi’. —40 ...
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