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Math Help - Application of linear approximnation

  1. #1
    Newbie
    Joined
    May 2009
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    3

    Application of linear approximnation

    Also this question which I kind of know how to do but can't get anywhere:
    The profit P for a cerain manufacturer selling x items is
    P(x) = 200xe^(-x/400)
    Use calculus to estimate the change in P as the number of items changes from x=100 to x=105 items.

    Thanks
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  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    408

    Stupid problem

    P'(x)=e^{-x/400}(200-x/2) So, P'(100)=150e^{-1/4}\approx 116.82011746071 Since the function at this point x=100 can be approximated by a line of this slope, \Delta P\approx P'(100)\Delta x \approx 117*5 = 585

    This problem is stupid. It's two and a half times harder than just plugging in the two values outright and it's off by about 2%
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