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Math Help - Need help solving this equation (may be factoring)?

  1. #1
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    Need help solving this equation (may be factoring)?

    Hi, in math class, we were assigned a challenge problem that has to do with finding the volume of a box. My function is:

    f(x) = 4x3 - 88x2 + 480x

    I found that the maximum value of this function is 768 (the maximum volume), but I want to know how to solve for `x`. This is what I have:
    768 = 4x3 - 88x2 + 480x
    192 = x3 - 22x2 + 120x

    How would I continue to solve for `x`?
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  2. #2
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    Re: Need help solving this equation (may be factoring)?

    How did you get your answer of 768? It should actually be about 774 by the way.

    Have you learnt about differentiation?
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  3. #3
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    Re: Need help solving this equation (may be factoring)?

    Quote Originally Posted by Flurite View Post
    Hi, in math class, we were assigned a challenge problem that has to do with finding the volume of a box. My function is:

    f(x) = 4x3 - 88x2 + 480x

    I found that the maximum value of this function is 768 (the maximum volume), but I want to know how to solve for `x`. This is what I have:
    768 = 4x3 - 88x2 + 480x
    192 = x3 - 22x2 + 120x

    How would I continue to solve for `x`?
    how did you find that the maximum volume is 768?

    I get approximately 774.
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  4. #4
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    Re: Need help solving this equation (may be factoring)?

    I used my graphing calculator, but then I just realized that decimals are involved too. All I need is the `x` value and I can't find that in my table.
    Last edited by Flurite; April 17th 2012 at 03:17 PM.
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  5. #5
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    Re: Need help solving this equation (may be factoring)?

    graph the volume and find the maximum ... it will give you the max volume (y-value) and x-value where that maximum occurs.
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  6. #6
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    Re: Need help solving this equation (may be factoring)?

    Found out how to change the maximum and minimum values to shift where the graph is showing. Thanks all!
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