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Math Help - maximum volume of a box

  1. #1
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    maximum volume of a box

    I have the volume equation as

    V=510x-1/2x^3

    then dv/dx = 0 therefore 510-3/2x^2=0

    solving for x gives x= + or - (sqrt340)

    (d^2v)/(dx^2)= -3x

    when x = +(sqrt340)
    (d^2v)/(dx^2)= negative therefore maximum

    V=510(sqrt340)-0.5(sqrt340)^3 = 6269 m^3

    I am not sure about the last part is it just a case of substituting the max x value obtained into the original volume formula?
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  2. #2
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    Quote Originally Posted by jlaing View Post
    I have the volume equation as

    V=510x-1/2x^3

    then dv/dx = 0 therefore 510-3/2x^2=0

    solving for x gives x= + or - (sqrt340)

    (d^2v)/(dx^2)= -3x

    when x = +(sqrt340)
    (d^2v)/(dx^2)= negative therefore maximum

    V=510(sqrt340)-0.5(sqrt340)^3 = 6269 m^3

    I am not sure about the last part is it just a case of substituting the max x value obtained into the original volume formula?
    to calculate the maximum volume, yes.
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