Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Question
Chapter 2.5, Problem 34S
To determine
To find: The derivative of the given function.
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Check out a sample textbook solutionStudents have asked these similar questions
In Exercises 13–32, findthe derivative of the function.
y = (2x − 7)3
Each of Exercises 25–36 gives a formula for a function y = f(x). In
each case, find f-x) and identify the domain and range of f-. As a
check, show that f(fx)) = f-"f(x)) = x.
25. f(x) = x
26. f(x) = x, x20
%3D
%3D
27. f(x) = x + 1
28. f(x) = (1/2)x – 7/2
30. f(x) = 1/r, x * 0
%3D
29. f(x) = 1/x, x>0
x + 3
31. f(x)
32. f(x) =
VE - 3
34. f(x) = (2x + 1)/5
2
33. f(x) = x - 2r, xs1
(Hint: Complete the square.)
* + b
x - 2'
35. f(x) =
b>-2 and constant
36. f(x) = x?
2bx, b> 0 and constant, xsb
Use Definition 0.10 to show that each pair of functions in
Exercises 67–70 are inverses of each other.
1
2
67. f(x) =2 – 3x and g(x) = -x+ 3
68. f(x) = x² restricted to [0, 0) and g(x) = V
69. f(x) =
and g(x) =
1+x
1-x
1
1
70. f(x) =
and g(x)
2x
2x
Chapter 2 Solutions
Calculus
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- Each of Exercises 81–84 shows the graphs of the first and second derivatives of a function y = f(x). Copy the picture and add to it a sketch of the approximate graph of f, given that the graph passes through the point P.arrow_forwardIn Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!arrow_forwardIn Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see. 63. a. y = tan-1 (tan x) b. y = tan (tan-1 x) 64. a. y = sin-1 (sin x) b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)arrow_forward
- In Exercises 69–76, graph each function, not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation. 69. y = -sqrt(2x + 1) 70. y =sqrt(1-x/2) 71. y = (x - 1)3 + 2 72. y = (1 - x)3 + 2 73. y = 1 /2x - 1 74. y=(2/x2)+1 72. y = (1 - x)3 + 2 75. y = -(x )^(1/3) 76. y = (-2x)^(2/3)arrow_forwardSometimes a derivative contains negative exponents, andsimplification requires that all exponents be positive.Write each of the expressions in Exercises 46–49 withoutnegative exponents.arrow_forwardIn Exercises 139–142, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. x2 – 25 = x - 5 5 139. X - x? + 7 140. = x? + 1 7 7 domain of f(x) = is x(x – 3) + 5(x - 3) 141. The (-0, 3) U (3, 0). 142. The restrictions on the values of x when performing the division f(x) h(x) g(x) k (x) are g(x) + 0, k(x) # 0, and h(x) + 0.arrow_forward
- In Exercises 173–176, use theresult of Exercise 172 to find the derivative of the function. h(x)=|x| \cos xarrow_forwardIn Exercises 13–24, compute the derivative using derivative rules that have been introduced so far.arrow_forwardExercises 63–86: Use transformations to sketch a graph of f. 63. f(x) = x² – 3 64. f(x) = -x² 65. f(x) = (x = 5)² + 3 66. f(x) = (x + 4)° 67. flx) = -Vx 68. f(x) = 2(x = 1F + 1 69. f(x) = -x² + 4 70. f(x) = V=x 71. f(x) = |x| – 4 73. f(x) = Vx – 3 + 2 74. f(x) = |x + 2| – 3 72. flx) = Vx + 1 76. flx) = |x| 78. f(x) = 2Vx – 2 - 1 75. f(x) = |2x| 77. f(x) = 1 – Vx 79. f(x) = -Vī - x 81. f(x) = V-(x + 1) 80. f(x) = V-x – 1 82. f(x) = 2 + V-(x – 3) 83. f(x) = (x = 1) 84. f(x) = (x + 2) 85. f(x) = -x' 86. f(x) = (-x)' + 1arrow_forward
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