CalcAnswersCh3

CalcAnswersCh3 - (Answers to Exercises for Chapter 3:...

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(Answers to Exercises for Chapter 3: Derivatives) A.3.1 CHAPTER 3: DERIVATIVES SECTION 3.1: DERIVATIVES, TANGENT LINES, and RATES OF CHANGE 1) 30 2) a) ± fa () = 3 23 a ² 2 , or ± = a ² 2 a ² 2 ; Hint: Rationalize the numerator of the difference quotient. b) Point-Slope Form: y ± 5 = 3 10 x ± 9 , Slope-Intercept Form: y = 3 10 x + 23 10 c) Point-Slope Form: y ± 5 = ± 10 3 x ± 9 , Slope-Intercept Form: y = ± 10 3 x + 35 3) a) i. ± 4.3 cm sec , ii. ± 4.03 cm sec ; b) ± 4 cm sec SECTION 3.2: DERIVATIVE FUNCTIONS and DIFFERENTIABILITY 1) Hint: fx + h ± h = 1 x + h 2 ± 1 x 2 h ; ± = ² 2 x 3 2) Hint: gw + h ± h = 3 w + h 2 ± 5 w + h + 4 ² ³ ´ µ · ± 3 w 2 ± 5 w + 4 ² ³ µ h ; ± = 6 w ² 5 3) Hint: rx + h ± h = x 4 + 4 x 3 h + 6 x 2 h 2 + 4 xh 3 + h 4 ± x 4 h ; ± = 4 x 3
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(Answers to Exercises for Chapter 3: Derivatives) A.3.2 4) ± fx () = 6 x 1/3 , or 6 x 3 , ±± = ² 2 x 4/3 , or ² 2 x 4 3 , ±±± = 8 3 x 7/3 , or 8 3 x 7 3 , f 4 x = ± 56 9 x 10/3 , or ± 56 9 x 10 3 5) 0 6) a) vt = 12 t 2 + 30 t ± 18 b) v 1 = 24 ft min , v 2 = 90 min , v 0 = ± 18 min c) at () = 24 t + 30 d) a 1 = 54 min 2 , a 2 = 78 min 2 , a 0 = 30 min 2 7) a) Yes; b) No; c) No; d) No (observe that p is discontinuous at ± 1 ); e) No; f) Yes 8) a) Yes, there is a vertical tangent line; a cusp b) Yes, there is a vertical tangent line; neither a corner nor a cusp c) No, there is not a vertical tangent line; a corner 9) a) ± 1 3 , 73 54 ² ³ ´ µ · and 2, ± 5 b) Point-Slope Form: y 5 2 ² ³ ´ µ · = ± 4 x ± 1 , Slope-Intercept Form: y = ± 4 x + 3 2 c) Point-Slope Form: y 5 2 ² ³ ´ µ · = 1 4 x ± 1 , Slope-Intercept Form: y = 1 4 x ± 11 4 d) 3, ± 1 2 ² ³ ´ µ · and ± 4 3 , ± 85 27 ² ³ ´ µ ·
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(Answers to Exercises for Chapter 3: Derivatives) A.3.3 10) a) 10, 200 () and ± 10, 200 . Hint: Find the point(s) a , fa on the flight path where the slope of the tangent line there equals the slope of the line connecting the point and the target. b) ± 2,104 and 50, 2600 11)
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(Answers to Exercises for Chapter 3: Derivatives) A.3.4 SECTION 3.3: TECHNIQUES OF DIFFERENTIATION 1) a) 15 x 2 + 6 x 3 ± 1 2 x 3/2 + 1 18 x 2/3 , or 15 x 2 + 6 x 3 ± 1 2 x 3 + 1 18 x 2 3 () b) 13 5 ± t 2 , or 13 t ± 5 2 c) 4 z 3 ± 16 z ; this can be factored as 4 zz + 2 z ± 2 .
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This note was uploaded on 09/08/2011 for the course MATH 150 taught by Professor Bart during the Spring '06 term at Mesa CC.

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CalcAnswersCh3 - (Answers to Exercises for Chapter 3:...

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