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Math Help - Another application of differentiation question

  1. #1
    Junior Member silvercats's Avatar
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    Another application of differentiation question

    total cost for a bus to run for one hour is 90+(v/10) .v is speed of the bus..
    take "C" as the cost for bus to run 1Km.What is the speed(v ) need for bus to make the cost minimum

    Here what i did:
    C=[ 90+(v/10) ] v -this is the cost for bus to run one hour.
    Dc/Dv= 90 + 3v/10
    set to zero and solve
    v=√-300 O.o

    answer has to be 30 as books says
    help
    thanks
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Re: Another application of differentiation question

    You're derivative is a bit off

    If \displaystyle C=90v+\frac{v^3}{10}\implies \frac{dC}{dv} = 90+\frac{3v^2}{10}

    I don't think the initial equation is correct either.
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  3. #3
    Junior Member silvercats's Avatar
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    Re: Another application of differentiation question

    thanks .
    What is the correct initial equation then?
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