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anonymous

  • 5 years ago

http://edugen.wiley.com/edugen/courses/crs4196/art/qb/qu/ch0/EAT_1227298660014_0_33367326491234830.gif Thats the graph of f' and assume f is continuous and f(0)=0 Find f(3)

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  1. anonymous
    • 5 years ago
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    Well, what does the value of f' tell you about f?

  2. anonymous
    • 5 years ago
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    its the derivative?

  3. anonymous
    • 5 years ago
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    Sweethert, keep it in chat please. this is for mmonish's question.

  4. anonymous
    • 5 years ago
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    Yes, but what does the derivative tell you? What does it mean to be the derivative?

  5. anonymous
    • 5 years ago
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    i have no idea..HELP

  6. anonymous
    • 5 years ago
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    What is the derivative of the function f(x) = 5x + 3?

  7. anonymous
    • 5 years ago
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    5

  8. anonymous
    • 5 years ago
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    slope?

  9. myininaya
    • 5 years ago
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    I can't see your graph

  10. anonymous
    • 5 years ago
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    Right. The derivative is the slope of the curve at any given x value.

  11. anonymous
    • 5 years ago
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    So, if the derivative is a constant, what does that mean about the curve of the original function?

  12. anonymous
    • 5 years ago
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    @myinninaya: i don't know y @polpak: the slope is ?

  13. anonymous
    • 5 years ago
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    The slope is a constant.

  14. anonymous
    • 5 years ago
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    What does the graph of f(x) = 5x+3 look like?

  15. anonymous
    • 5 years ago
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    a line

  16. myininaya
    • 5 years ago
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    yes

  17. anonymous
    • 5 years ago
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    Right, and you can see that if you take the derivative of a line you will get a constant value for the slope. \(y = mx + b \implies y' = m\)

  18. anonymous
    • 5 years ago
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    yea

  19. anonymous
    • 5 years ago
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    So look at the graph of f'. What is f' from x=0 to x=2?

  20. anonymous
    • 5 years ago
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    straight line...so slope is 0

  21. myininaya
    • 5 years ago
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    so you see a horizontal line?

  22. anonymous
    • 5 years ago
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    yea

  23. anonymous
    • 5 years ago
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    No, the value of f' over that interval is constantly 1. f' = 1 on the interval from 0 to 2.

  24. anonymous
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    Which means that f must have a constant slope of 1 over that interval.

  25. anonymous
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    ok

  26. anonymous
    • 5 years ago
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    So if f(0) = 0, what will f(2) be?

  27. anonymous
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    1?

  28. anonymous
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    No. Imagine a line with a slope of 1, that goes through the origin.

  29. anonymous
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    Where will that line cross the x=2 line?

  30. anonymous
    • 5 years ago
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    1/2

  31. anonymous
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    Each time x increases by 1, the function increases by 1. That's what it means to have a slope of 1. \(\frac{\text{change in f(x)}}{\text{change in x}}\)

  32. anonymous
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    = 1

  33. anonymous
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    As much as x changes, the function changes.

  34. anonymous
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    So if f(0) = 0, f(2) = ?

  35. anonymous
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    1/2

  36. anonymous
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    \(\frac{\Delta f}{\Delta x} = 1.\) \(\Delta x = 2 \implies \Delta f =?\)

  37. anonymous
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    How much did x change from 0 to 2?

  38. anonymous
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    2

  39. anonymous
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    The function must also have changed by the same amount if the ratio equals 1

  40. anonymous
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    So how much does the function change over that same interval?

  41. anonymous
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    2?

  42. anonymous
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    Yes

  43. anonymous
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    2/2 = 1 = the slope.

  44. anonymous
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    So now we know f(2). What do we know about the slope over the interval from x=2 to x=3?

  45. anonymous
    • 5 years ago
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    its negative?

  46. anonymous
    • 5 years ago
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    Negative what specifically?

  47. anonymous
    • 5 years ago
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    slope

  48. anonymous
    • 5 years ago
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    We have a graph of f'. The value of f' is the slope of f.

  49. anonymous
    • 5 years ago
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    What is the value of f' from x=2 to x=3?

  50. anonymous
    • 5 years ago
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    -1

  51. anonymous
    • 5 years ago
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    What is the slope of f from x=2 to x = 3?

  52. anonymous
    • 5 years ago
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    It's not a trick question =)

  53. anonymous
    • 5 years ago
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    The value of f' is the slope of f.

  54. anonymous
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    -1

  55. anonymous
    • 5 years ago
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    Right.

  56. anonymous
    • 5 years ago
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    So if the slope of f is -1 from 2 to 3. And the \(\frac{\text{Change of f}}{\text{Change of x}}\) = Slope = -1, What is the change in x? What is the change in f?

  57. anonymous
    • 5 years ago
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    1

  58. anonymous
    • 5 years ago
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    1 is which?

  59. anonymous
    • 5 years ago
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    x

  60. anonymous
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    Right. So \[\frac{\text{Change in f}}{\text{Change in x}} = -1\] \[\frac{\text{Change in f}}{1} = -1\] Change in f =?

  61. anonymous
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    -1

  62. anonymous
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    Right. So f(2) = 2, and from 2 to 3, the slope of f is -1, then the value of f will change by -1, what is f(3)?

  63. anonymous
    • 5 years ago
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    -2?

  64. anonymous
    • 5 years ago
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    Is any of this making sense?

  65. anonymous
    • 5 years ago
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    No f changes by -1. It goes down 1.

  66. anonymous
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    f goes down 1 every time x goes up 1. That's what it means to have a -1 slope. Just like having a slope of 1 means that f goes up 1 each time x goes up 1.

  67. anonymous
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    -1

  68. anonymous
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    So if f(2) = 2, and x goes up 1, what will f do?

  69. anonymous
    • 5 years ago
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    f(3)=3

  70. anonymous
    • 5 years ago
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    Your answers are all over the place. I'm not sure what is confusing you about what I'm asking, but clearly something is out of sync. Do you understand what I'm saying about slope?

  71. anonymous
    • 5 years ago
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    If I have a line g(x) = x. What is the slope?

  72. anonymous
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    1

  73. anonymous
    • 5 years ago
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    Ok, and what is g(2) and g(4) and g(5)?

  74. anonymous
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    2,4,5

  75. anonymous
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    Ok. And on the interval from x=2 to x=4, how much does x increase?

  76. anonymous
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    2

  77. anonymous
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    And g(x) over that interval increases how much?

  78. anonymous
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    2?

  79. anonymous
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    Yes

  80. anonymous
    • 5 years ago
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    Change in g = g(4)-g(2)

  81. anonymous
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    just like change in x was 4-2

  82. anonymous
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    So as x increases by 1 , g increases by 1. That is what it means to have a slope of 1.

  83. anonymous
    • 5 years ago
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    If we have h(x) = 2x, What is the slope?

  84. anonymous
    • 5 years ago
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    i hope you know that this is an antiderivative problem

  85. anonymous
    • 5 years ago
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    I do.

  86. anonymous
    • 5 years ago
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    But there are some small holes in your understanding that make solving these very easy. If I fill the holes you can answer all these in less than a minute.

  87. anonymous
    • 5 years ago
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    oh cool

  88. anonymous
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    What is the slope of h?

  89. anonymous
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    2

  90. anonymous
    • 5 years ago
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    So what is h(2), h(4), and h(5)?

  91. anonymous
    • 5 years ago
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    4,8,10

  92. anonymous
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    So each time x increases by 1, h increases by how much?

  93. anonymous
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    2

  94. anonymous
    • 5 years ago
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    And what is the derivative of h?

  95. anonymous
    • 5 years ago
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    2

  96. anonymous
    • 5 years ago
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    So if I tell you that j(0) = 1, and the derivative of j (also called j') = 5, Can you tell me what j(3) =?

  97. anonymous
    • 5 years ago
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    (remember that the derivative is the slope)

  98. anonymous
    • 5 years ago
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    15

  99. anonymous
    • 5 years ago
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    Very nearly.

  100. anonymous
    • 5 years ago
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    That would be the correct answer if j(0) = 0

  101. anonymous
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    5x+15

  102. anonymous
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    But because j(0) = 1, we need to start at one, and add 15 because the change in x is 3 and the slope is 5.

  103. anonymous
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    16?

  104. anonymous
    • 5 years ago
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    Yes

  105. anonymous
    • 5 years ago
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    Now. If I tell you that f(0) = 0 and the derivative ( also called slope, and f') is 1 from 0 to 2, what is f(2) again?

  106. anonymous
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    2

  107. anonymous
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    And now if we know that f(2) = 2, and f' = -1 from 2 to 3, what is f(3)?

  108. anonymous
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    1

  109. anonymous
    • 5 years ago
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    Yes!

  110. anonymous
    • 5 years ago
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    so thats the answer

  111. anonymous
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    Yes

  112. anonymous
    • 5 years ago
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    ok dont help me solve this but let me know if i did it correctly

  113. anonymous
    • 5 years ago
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    Ok

  114. anonymous
    • 5 years ago
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    f(7)

  115. anonymous
    • 5 years ago
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    oh pellet my boss is here...ill ttyl..thanks a ton

  116. anonymous
    • 5 years ago
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    lol, k. You can repost the answer here and I'll check back

  117. anonymous
    • 5 years ago
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    ok thankls

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