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burhan101

  • 2 years ago

Determine the extreme values:

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

  2. fozia
    • 2 years ago
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    values maximum, minimum

  3. burhan101
    • 2 years ago
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    yes, how tho?

  4. burhan101
    • 2 years ago
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    i find the derivative first and then what?

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

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

  7. fozia
    • 2 years ago
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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

  8. burhan101
    • 2 years ago
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    @fozia wait, you and I got different derivatives

  9. tcarroll010
    • 2 years ago
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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. burhan101
    • 2 years ago
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  11. Abhishek619
    • 2 years ago
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    check if the function is increasing or decreasing?

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

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  13. burhan101
    • 2 years ago
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    how do i check if its inc/dec?

  14. Abhishek619
    • 2 years ago
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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.

  15. tcarroll010
    • 2 years ago
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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.

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

  17. tcarroll010
    • 2 years ago
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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.

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

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

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

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

  22. burhan101
    • 2 years ago
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    & yes i am using the quotient rule

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

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

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

  26. burhan101
    • 2 years ago
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    ohhhh is see it

  27. tcarroll010
    • 2 years ago
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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.

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

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

  30. tcarroll010
    • 2 years ago
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    All good now, @burhan101 ?

  31. burhan101
    • 2 years ago
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    yes thanks !!

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

  33. burhan101
    • 2 years ago
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    thank you very much, you do explain things very clear !

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

  35. burhan101
    • 2 years ago
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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

  36. dan815
    • 2 years ago
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    YO BURHAANN MY BRO

  37. dan815
    • 2 years ago
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    are u done with this equation

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

  39. dan815
    • 2 years ago
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    explain the meaning of an extreme value to me

  40. burhan101
    • 2 years ago
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    an absolute mx or an absolute min

  41. dan815
    • 2 years ago
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    ok

  42. dan815
    • 2 years ago
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    so that means the slope there is 0

  43. burhan101
    • 2 years ago
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    yes

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

  45. dan815
    • 2 years ago
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    first solve f'(x) = 0

  46. dan815
    • 2 years ago
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    |dw:1371749721969:dw|

  47. burhan101
    • 2 years ago
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    so i solve for x

  48. dan815
    • 2 years ago
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    yes

  49. dan815
    • 2 years ago
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    okay lemme give u some simpler exmaples

  50. dan815
    • 2 years ago
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    |dw:1371749857123:dw|

  51. dan815
    • 2 years ago
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    what are the extreme values for a parabola

  52. burhan101
    • 2 years ago
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    the vertex

  53. dan815
    • 2 years ago
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    okay and the slope there is?

  54. burhan101
    • 2 years ago
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    0

  55. dan815
    • 2 years ago
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    so that means the derivative there is?

  56. burhan101
    • 2 years ago
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    |dw:1371749935529:dw|

  57. dan815
    • 2 years ago
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    what nooo

  58. burhan101
    • 2 years ago
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    ohh:(

  59. dan815
    • 2 years ago
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    0/8 = 0|dw:1371749995868:dw|

  60. burhan101
    • 2 years ago
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    0=cos4x?

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

  62. dan815
    • 2 years ago
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    hello bahrom jhanny wants us to play a game

  63. burhan101
    • 2 years ago
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    what's the next step ..

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

  65. dan815
    • 2 years ago
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    must*

  66. dan815
    • 2 years ago
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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

  67. burhan101
    • 2 years ago
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    okay

  68. burhan101
    • 2 years ago
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    would i keep my calculator in degrees or radians?

  69. dan815
    • 2 years ago
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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

  70. burhan101
    • 2 years ago
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    |dw:1371751462417:dw|

  71. Loser66
    • 2 years ago
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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.

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

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