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onegirl

Check the hypotheses of Rolle’s Theorem and the Mean Value Theorem and find a value of c that makes the appropriate conclusion true. Illustrate the conclusion with a graph. f(x) = sin x , [0,pi/2]

  • one year ago
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  1. onegirl
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    @Mertsj can u help?

    • one year ago
  2. onegirl
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    @experimentX how would i do this one?

    • one year ago
  3. experimentX
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    let f(x) = sin(x) then f'(x) = ?

    • one year ago
  4. onegirl
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    okay

    • one year ago
  5. onegirl
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    cos(x)

    • one year ago
  6. experimentX
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    when is cos(x) zero?

    • one year ago
  7. onegirl
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    zero? you said find the derivative of sinx right?

    • one year ago
  8. experimentX
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    yes ... at what point is cos(x) equal to zero?

    • one year ago
  9. onegirl
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    there is not point where it is equal to zero

    • one year ago
  10. experimentX
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    why not?

    • one year ago
  11. onegirl
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    when i graph it...it doesn't

    • one year ago
  12. experimentX
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    you got the wrong graph then.

    • one year ago
  13. onegirl
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    |dw:1363197320465:dw| thats how it looks liek ohh okay

    • one year ago
  14. experimentX
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    |dw:1363197334937:dw|

    • one year ago
  15. onegirl
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    ok

    • one year ago
  16. experimentX
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    |dw:1363197397226:dw|

    • one year ago
  17. onegirl
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    yea it is

    • one year ago
  18. onegirl
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    okay i got it

    • one year ago
  19. experimentX
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    so ... what's the point?

    • one year ago
  20. onegirl
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    (0,1) ?

    • one year ago
  21. experimentX
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    no ...

    • one year ago
  22. experimentX
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    http://www.wolframalpha.com/input/?i=plot+cos%28x%29+from+-2pi+to+2pi

    • one year ago
  23. onegirl
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    so its more than 1?

    • one year ago
  24. onegirl
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    0,1.5 ?

    • one year ago
  25. experimentX
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    NOOOOOOOOOOOOOOO http://www.wolframalpha.com/input/?i=solve+cos%28x%29+%3D+0+for+x+between+0+and+pi

    • one year ago
  26. onegirl
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    so its 1.57080?

    • one year ago
  27. experimentX
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    |dw:1363198158808:dw|

    • one year ago
  28. onegirl
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    ok

    • one year ago
  29. experimentX
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    so pick any two points above pi/2 and below pi/2

    • one year ago
  30. onegirl
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    okay? do you do this different than the las tone tho? i'm not gonna use f(a) - f(b)/ b - a ?

    • one year ago
  31. experimentX
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    |dw:1363198343133:dw|

    • one year ago
  32. onegirl
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    ohh ok

    • one year ago
  33. experimentX
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    |dw:1363198401986:dw|

    • one year ago
  34. onegirl
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    ok

    • one year ago
  35. experimentX
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    |dw:1363198546707:dw| do you get that?

    • one year ago
  36. onegirl
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    yes i do

    • one year ago
  37. experimentX
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    Okay i gotta go ...

    • one year ago
  38. onegirl
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    ok thx

    • one year ago
  39. experimentX
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    |dw:1363198676612:dw|

    • one year ago
  40. onegirl
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    okay

    • one year ago
  41. onegirl
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    So i filled in those a b c's and here i got....f(pi/2) = f(3pi/4) - f(pi/4) over 3pi/4 - pi/4

    • one year ago
  42. onegirl
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    f(3pi/4) = 3pi^2 + 1 = ?

    • one year ago
  43. onegirl
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    can u tell me if i plugged it right @experimentX ?

    • one year ago
  44. experimentX
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    yes that's correct.

    • one year ago
  45. experimentX
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    \[ f(3 \pi /4) = \sin(3\pi/4) = 1/ \sqrt 2 \] Find the value of f(pi/4) from your calculator or wolfram.

    • one year ago
  46. onegirl
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    okay

    • one year ago
  47. onegirl
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    I got 1

    • one year ago
  48. experimentX
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    huh .. do it again, what is sin(pi/4) ... plug into wolfram.

    • one year ago
  49. onegirl
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    hold on

    • one year ago
  50. onegirl
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    1/sqrt(2)

    • one year ago
  51. onegirl
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    i got 1 over sqrt of 2

    • one year ago
  52. onegirl
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    what do i do next ?

    • one year ago
  53. experimentX
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    yes ... plug into your Rolle's condition.

    • one year ago
  54. onegirl
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    the formula right?

    • one year ago
  55. onegirl
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    so f(1/sqrt(2) - f(1/sqrt(2)/ 1/sqrt(2) - 1/sqrt(2) ?

    • one year ago
  56. experimentX
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    no ...

    • one year ago
  57. experimentX
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    |dw:1363384214639:dw|

    • one year ago
  58. onegirl
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    ohh ok

    • one year ago
  59. onegirl
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    how do i solve that?

    • one year ago
  60. onegirl
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    so it will be 3/3 right?

    • one year ago
  61. experimentX
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    |dw:1363384415083:dw|

    • one year ago
  62. onegirl
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    okay

    • one year ago
  63. onegirl
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    so those will be the numerator?

    • one year ago
  64. experimentX
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    yes ... you just found out the value. Do you know what is functional notation?

    • one year ago
  65. onegirl
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    no

    • one year ago
  66. experimentX
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    yeah ... that is the problem. you haven't advanced to the point of doing this. let f(x) = cos(x), what is value of f(0)

    • one year ago
  67. onegirl
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    f(x) = 1

    • one year ago
  68. experimentX
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    yep ... if f(x) = sin(x) ,,, then what is f(pi/4) ??

    • one year ago
  69. onegirl
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    1 over sqrt(2)

    • one year ago
  70. experimentX
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    yes ... what is f(3pi/4) ??

    • one year ago
  71. onegirl
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    its the same 1 over sqrt(2)

    • one year ago
  72. experimentX
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    yes ... plug in those values in |dw:1363385976116:dw|

    • one year ago
  73. onegirl
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    plug them in the denominator?

    • one year ago
  74. experimentX
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    |dw:1363386098600:dw|

    • one year ago
  75. onegirl
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    ohh okay hold on

    • one year ago
  76. onegirl
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    f(1/sqrt(2) - f(1/sqrt(2) over 3pi/4 - pi/4

    • one year ago
  77. experimentX
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    No no ... what are you dong?? why are you putting 1/sqrt(2) inside function?

    • one year ago
  78. onegirl
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    you said to plug them in?

    • one year ago
  79. experimentX
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    yes .. |dw:1363386528821:dw|

    • one year ago
  80. onegirl
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    okay

    • one year ago
  81. onegirl
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    i'll ask my teacher on this one thanks for your help.

    • one year ago
  82. experimentX
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    |dw:1363387122187:dw|

    • one year ago
  83. onegirl
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    so i plug those in pi?

    • one year ago
  84. experimentX
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    no ... you just calculated those values. plug them in.

    • one year ago
  85. onegirl
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    I just did and you told me it was incorrect..i'm confused

    • one year ago
  86. experimentX
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    yes ... this is where you got confused.

    • one year ago
  87. onegirl
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    ok

    • one year ago
  88. experimentX
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    |dw:1363387985440:dw|

    • one year ago
  89. onegirl
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    ohh ok

    • one year ago
  90. experimentX
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    what is the value of|dw:1363388256685:dw|

    • one year ago
  91. onegirl
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    0?

    • one year ago
  92. experimentX
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    yes ... so |dw:1363388362361:dw|

    • one year ago
  93. onegirl
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    the derivative of it?

    • one year ago
  94. experimentX
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    yes ... is there a point where derivative is zero?

    • one year ago
  95. onegirl
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    yea

    • one year ago
  96. experimentX
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    what is that point?

    • one year ago
  97. onegirl
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    umm at 0, 0?

    • one year ago
  98. experimentX
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    No ..

    • one year ago
  99. onegirl
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    idk

    • one year ago
  100. experimentX
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    we talked about that in the above posts. check again ... the point is pi/2

    • one year ago
  101. onegirl
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    ohh yes okay

    • one year ago
  102. onegirl
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    so it reached 0 at pi/2

    • one year ago
  103. experimentX
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    no ... the derivative is zero at pi/2

    • one year ago
  104. onegirl
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    ok

    • one year ago
  105. experimentX
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    gotta go ... you gotta work harder.

    • one year ago
  106. experimentX
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    good luck!!

    • one year ago
  107. onegirl
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    ok well can u tell me what i should do next before you go

    • one year ago
  108. experimentX
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    you wanted to verify Rolle's theorem, which you did.

    • one year ago
  109. onegirl
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    yea its continuos and differentiable i know that

    • one year ago
  110. experimentX
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    what do you want to do?

    • one year ago
  111. onegirl
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    find a value for c

    • one year ago
  112. onegirl
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    so this could be true a < c < b

    • one year ago
  113. experimentX
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    of course it is ..

    • one year ago
  114. experimentX
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    |dw:1363389508215:dw|

    • one year ago
  115. onegirl
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    ok so c is pi/2 ?

    • one year ago
  116. experimentX
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    |dw:1363389556563:dw|

    • one year ago
  117. onegirl
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    ohhh ok

    • one year ago
  118. onegirl
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    so c is 2pi/4

    • one year ago
  119. experimentX
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    yes

    • one year ago
  120. onegirl
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    ok

    • one year ago
  121. experimentX
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    any probs??

    • one year ago
  122. onegirl
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    no thx

    • one year ago
  123. experimentX
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    see you around ... gotta go offline :)

    • one year ago
  124. onegirl
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    ok

    • one year ago
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