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burhan101

Determine the extreme values:

  • 10 months ago
  • 10 months ago

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  1. burhan101
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    \[\huge y= \frac{ e^{x} }{ 1+e^{x} }, x \epsilon [0,4]\]

    • 10 months ago
  2. fozia
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    values maximum, minimum

    • 10 months ago
  3. burhan101
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    yes, how tho?

    • 10 months ago
  4. burhan101
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    i find the derivative first and then what?

    • 10 months ago
  5. fozia
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    first fint derivative that gives the result y'=ex/(1+ex)2 then eqaute it to zero gives ex=0

    • 10 months ago
  6. burhan101
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    \[\huge y'=\frac{ e^x }{ (1+e^x) }\]

    • 10 months ago
  7. fozia
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    take 2nd derivatv now put the value of x =0 in 2nd derivativ if relt is postv then its min otherwise max

    • 10 months ago
  8. burhan101
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    @fozia wait, you and I got different derivatives

    • 10 months ago
  9. tcarroll010
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    @fozia , you have correctly identified the first derivative, but it will never be equal to zero. Therefore, there is no need to take the second derivative. It is sufficient to just analyze the first derivative, realize that it is always positive, and that the original function is always increasing, so it has no extreme values.

    • 10 months ago
  10. burhan101
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    • 10 months ago
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  11. Abhishek619
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    check if the function is increasing or decreasing?

    • 10 months ago
  12. tcarroll010
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    Here's a graph to show you that it is always increasing

    • 10 months ago
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  13. burhan101
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    how do i check if its inc/dec?

    • 10 months ago
  14. Abhishek619
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    its first derivative is always a positive, hence it is increasing for all [0.4]. the minimum value will be at x=0, maximu will be at x=4.

    • 10 months ago
  15. tcarroll010
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    Read my first post. That will tell you. That numerator of the first derivative is always positive. So is the denominator.

    • 10 months ago
  16. tcarroll010
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    No extreme values for domain of all x. min and max though at the endpoints for the given problem domain.

    • 10 months ago
  17. tcarroll010
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    That's because "e" is a positive base, so any exponent you put on it will result in a positive number.

    • 10 months ago
  18. tcarroll010
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    Do you see that fozia's derivative is correct? That's where you should start.

    • 10 months ago
  19. tcarroll010
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    Use the quotient rule to get the derivative. Do you need help with that?

    • 10 months ago
  20. tcarroll010
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    @burhan101 I have 2 pending questions posted for you here.

    • 10 months ago
  21. burhan101
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    @tcarroll010 im trying to figure out how that derivative is right

    • 10 months ago
  22. burhan101
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    & yes i am using the quotient rule

    • 10 months ago
  23. burhan101
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    \[\huge \frac{ (1+e^x)(e^x)-(e^x)(e^x)}{ (1+e^x)^2 }\]

    • 10 months ago
  24. tcarroll010
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    \[\frac{ (1 + e ^{x})e ^{x} - e ^{x}e ^{x} }{ (1 + e ^{x})^{2} } = \frac{ e ^{x} + e ^{2x} - e ^{2x} }{ (1 + e ^{x})^{2} }\]

    • 10 months ago
  25. tcarroll010
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    In the numerator, you are left with only e^x and the denominator is the original denominator squared.

    • 10 months ago
  26. burhan101
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    ohhhh is see it

    • 10 months ago
  27. tcarroll010
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    So, there is no need to take the second derivative. It is sufficient to just analyze the first derivative, realize that it is always positive, and that the original function is always increasing, so it has no extreme values, if your domain is all x. But your domain is limited, so you have your min and max at the x-value endpoints.

    • 10 months ago
  28. burhan101
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    but dont i plug in 0 and 4 in f(x) ?

    • 10 months ago
  29. tcarroll010
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    So, min at: e^0 / (1 + e^0) max at: e^4 / (1 + e^4)

    • 10 months ago
  30. tcarroll010
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    All good now, @burhan101 ?

    • 10 months ago
  31. burhan101
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    yes thanks !!

    • 10 months ago
  32. tcarroll010
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    uw! Good luck in all of your studies and thx for the recognition! @burhan101

    • 10 months ago
  33. burhan101
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    thank you very much, you do explain things very clear !

    • 10 months ago
  34. tcarroll010
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    I just like to help. Kind words on your part!

    • 10 months ago
  35. burhan101
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    For this function \[\huge f(x)= 2\sin4x+3 ; [0, \pi]\] i get the derivative as \[\huge f'(x)=8\cos4x \] To find the extreme values, do i plug in the endpoints into f(x) ? @tcarroll010

    • 10 months ago
  36. dan815
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    YO BURHAANN MY BRO

    • 10 months ago
  37. dan815
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    are u done with this equation

    • 10 months ago
  38. burhan101
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    dannn:) ! no im not, do i plug the endpoints into the function ?

    • 10 months ago
  39. dan815
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    explain the meaning of an extreme value to me

    • 10 months ago
  40. burhan101
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    an absolute mx or an absolute min

    • 10 months ago
  41. dan815
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    ok

    • 10 months ago
  42. dan815
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    so that means the slope there is 0

    • 10 months ago
  43. burhan101
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    yes

    • 10 months ago
  44. dan815
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    but u must check the end points too incase its just a local max or local min there

    • 10 months ago
  45. dan815
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    first solve f'(x) = 0

    • 10 months ago
  46. dan815
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    |dw:1371749721969:dw|

    • 10 months ago
  47. burhan101
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    so i solve for x

    • 10 months ago
  48. dan815
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    yes

    • 10 months ago
  49. dan815
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    okay lemme give u some simpler exmaples

    • 10 months ago
  50. dan815
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    |dw:1371749857123:dw|

    • 10 months ago
  51. dan815
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    what are the extreme values for a parabola

    • 10 months ago
  52. burhan101
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    the vertex

    • 10 months ago
  53. dan815
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    okay and the slope there is?

    • 10 months ago
  54. burhan101
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    0

    • 10 months ago
  55. dan815
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    so that means the derivative there is?

    • 10 months ago
  56. burhan101
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    |dw:1371749935529:dw|

    • 10 months ago
  57. dan815
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    what nooo

    • 10 months ago
  58. burhan101
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    ohh:(

    • 10 months ago
  59. dan815
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    0/8 = 0|dw:1371749995868:dw|

    • 10 months ago
  60. burhan101
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    0=cos4x?

    • 10 months ago
  61. dan815
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    @bahrom7893 http://multiplayerchess.com/#!/5gqIqmm

    • 10 months ago
  62. dan815
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    hello bahrom jhanny wants us to play a game

    • 10 months ago
  63. burhan101
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    what's the next step ..

    • 10 months ago
  64. dan815
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    1what values of x wud make cos4x=0 think about cos pi/2=0 so what much it be

    • 10 months ago
  65. dan815
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    must*

    • 10 months ago
  66. dan815
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    ill give u one of the values that is in between 0 and pi cos(4(pi/8)) = 0 thats one

    • 10 months ago
  67. burhan101
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    okay

    • 10 months ago
  68. burhan101
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    would i keep my calculator in degrees or radians?

    • 10 months ago
  69. dan815
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    heyy dont be silly u shud know this stuff!! we been doing trig of a while remember where cosx graph = 0

    • 10 months ago
  70. burhan101
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    |dw:1371751462417:dw|

    • 10 months ago
  71. Loser66
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    @dan815 I don't know why everybody here ignores the ends of interval when they find out the max, min. My prof always asked us to consider those points, too.

    • 10 months ago
  72. dan815
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    i told him to look at those points too :) but its not really needed in this case

    • 10 months ago
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