chapter 1 answers - Chapter 1 The Derivative 1.1 The Slope...

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23 Chapter 1 The Derivative 1.1 The Slope of a Straight Line 1. 37 yx !" ; y -intercept: (0, 3), slope: ±7 2. 3 1 3 1 5 5 5 x # ! ! # ; y -intercept: 1 0, 5 $% &’ () , slope: 3 5 3. 3 1 3 23 2 2 2 x x y y y x # ! " * ! * ! # ; y -intercept: 3 0, 2 , slope: 1 2 4. 6 0 6 y y x ! * ! # ; y -intercept: (0, 6), slope: 0 5. 1 55 77 x y y x ! " * ! " ; y -intercept: (0, ±5), slope: 1 7 6. 4 1 4 1 4 9 1 9 9 9 x x y y y x "" # ! " * ! * ! " " ; y -intercept: 1 0, 9 " , slope = 4 9 " 7. slope = –1, (7, 1) on line. Let ( x , y ) = (7, 1), m = –1. + , 11 1 ( 7) 8 " ! " * " ! " " * ! " # y y m x x y x 8. slope = 2; (1, ±2) on line. Let ( x , y ) = (1, ±2), m = 2. + , 2 2( 1) 24 " ! " * # ! " * y y m x x y x 9. slope = 1 2 ; (2, 1) on line. +,+, 1 Let , 2,1 ; . 2 x y m !! +, 1 12 2 1 2 y y m x x y x " ! " * " ! " * ! 10. slope 7 ; 3 ! , 45 " on line. 1 2 7 Let , , ; . 4 5 3 x y m ! " ! 2 7 1 5 3 4 7 59 3 60 " ! " * # ! " * y y m x x y x 11. ,5 and , 4 $ % $ % & & ( ) ( ) on line. 21 5 5 10 7 7 7 4 5 9 63 slope 10 yy xx " " " " ! ! ! ! " " " " 5 63 Let , ,5 , . 7 10 x y m 63 5 5 10 7 y y m x x y x " ! " * " ! " 12. 1 ,1 2 $ % & ( ) and (1, 4) on line. 22 4 1 3 slope= 6 1 " " ! ! ! " " + , Let , (1,4), 6. x y m + , + , 4 6 1 62 y y m x x y x " ! " * " ! " * 13. (0, 0) and (1, 0) on line. 00 slope 0 10 0 0( 0) 0 y x y ! ! ! " ! " * ! 14. , 27 $ % & ( ) and 2 3 $ % & ( ) on line. + , 1 8 7 7 7 6 32 1 48 slope 49 m " ! ! ! ! ! " 2 Let , ,1 . 3 xy $ % ! & ( ) 48 2 1 49 3 48 17 49 49 y y m x x y x " ! " * " ! " * !# 15. Horizontal through (2, 9). Let ( , ) (2,9), ! m = 0 (horizontal line). + , + , 9 0 2 9 y y m x x y x y " ! " * " ! " * !
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24 Chapter 1: The Derivative 16. x -intercept is 1; y -intercept is –3. The intercepts (1, 0) and (0, –3) are on the line. 21 30 slope 3 01 yy m xx " " " ! ! ! ! "" y -intercept (0, b ) = (0, –3) 33 y mx b y x ! # * ! " 17. x -intercept is ; - " y -intercept is 1. The intercepts + , ,0 " and (0, 1) are on the line. 1 0 1 slope= 0 ( ) -- !! " " " y -intercept (0, b ) = (0, 1) 1 x y mx b y ! # * ! # 18. Slope = 2; x -intercept is –3. The x -intercept (–3, 0) is on the line. Let 11 ( , ) ( 3,0), 2. ! " ! x y m + , + , 0 2 3 26 y y m x x y x yx " ! " * " ! # * !# 19. Slope = ±2; x -intercept is –2. The x -intercept (–2, 0) is on the line. + , Let , ( 2,0), 2. x y m ! " ! + , + , 0 2 2 24 y y m x x y x " ! " * " ! " # * ! " " 20. Horizontal through + , 7,2 . + , + , Let , 7,2 , xy ! m = 0 (horizontal line). +, + , 2 0 7 2 y y m x x y x y " ! " * " ! " * ! 21. Parallel to y = x ; (2, 0) on line. + , Let , (2,0); ! slope = m = 1. + , + , 0 1 2 2 y y m x x y x " ! " * " ! " * !" 22. Parallel to x + 2 y = 0; (1, 2) on line. 2 0 ; 22 x y y x m # ! * ! " ! " + , Let , (1,2). ! 1 2 15 y y m x x y x " ! " * " ! " " * ! " # 23. Parallel to 37 ; x -intercept is 2. slope = m = 3. + , Let , (2, 0). ! + , + , 0 3 2 36 y y m x x y x " ! " * " ! " * 24. Parallel to 13 "! ; y -intercept is 0. 13 , slope = m = 1, b = 0. y mx b y x ! # * ! 25. Perpendicular to y + x = 0; (2, 0) on line. 1 1 2 2 2 0 slope 1 1 1 1 1 Let ( , ) (2,0). y x y x m m m m m # ! * ! " * ! ! " . ! " * " . ! " * ! ! + , 2 2 2 02 2 y y m x x y x " ! " * " ! " * 26. Perpendicular to 5 1; ! " # (1, 5) on line. slope = 1 5 m 1 2 2 2 1 1 5 1 5 m m m m . ! " * " ! " * ! Let ( , ) (1,5). ! 2 2 2 1 51 5 1 24 55 y y m x x y x " ! " * " ! " * 27. Start at (1, 0), then move one unit right and one unit up to (2, 1). 28. Start at (±1, 1), then move one unit up and two units to the right. 29. Start at (1, ±1), then move one unit up and three units to the left. Alternatively, move one unit down and three units to the right.
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Section 1.1 The Slope of a Straight Line 25 30. Start at (0, 2), then move zero units up and any distance (for example, one unit) right. 31. (a)–(C) x - and y -intercepts are 1. (b)–(B) x -intercept is 1, y -intercept is –1. (c)–(D) x - and y -intercepts are –1. (d)–(A) x -intercept is –1, y -intercept is 1. 32. 11 20 22 x y y x m # ! * ! " * ! " The slope of the line through (±1, 2) and (3, b ) is also 1 .
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chapter 1 answers - Chapter 1 The Derivative 1.1 The Slope...

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