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    notamaths_genius's Avatar
    notamaths_genius Posts: 6, Reputation: 1
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    #1

    Dec 1, 2007, 08:30 PM
    Differientiation Application
    I'm having difficulties on this question and I could use some help. Thanks

    A metal beam, 10 m long, is unevenly loaded. As a result it is bent slightly from the horizontal. The relationship between the deviation from the horizontal (D mm) and the distance along the beam (x m) is given by:

    D= [x(10-x)(x-20)]/1000
    At what point along the beam is the deviation from the horizontal maximum?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Dec 1, 2007, 09:16 PM
    Expand out D, then it's easy to differentiate.
    terryg752's Avatar
    terryg752 Posts: 197, Reputation: 4
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    #3

    Dec 1, 2007, 09:24 PM
    D` means first derivative, D`` 2nd derivative.

    For Maximum, D` = 0 and D`` = negative.

    D = [x(10-x)(x-20)]/1000

    1000 D = x (-x^2 + 30 x -200)

    = -x^3 +30 x^2 - 200x

    Differentiating:

    1000D` = -3x^2 +60 x- 200

    1000D`` = -6x + 60

    D` = 0 gives 2 two values of x

    For MAXIMUM, Select the value which makes D`` (Second derivative) negative value.
    notamaths_genius's Avatar
    notamaths_genius Posts: 6, Reputation: 1
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    #4

    Dec 1, 2007, 09:59 PM
    Which value of x do I find out... the second derative one, and from there then what? Thanks
    terryg752's Avatar
    terryg752 Posts: 197, Reputation: 4
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    #5

    Dec 1, 2007, 10:03 PM
    D` = 0

    means: -3x^2 +60 x- 200 = 0

    Get 2 values of x from this quadratic.

    Select one which makes D`` = (-6x + 60)/1000 NEGATIVE.
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