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mskyeg Group Title

Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(h – 10)(h – 8). What is the maximum volume for the domain 0 < h < 10? Round to the nearest cubic foot.

  • 2 years ago
  • 2 years ago

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  1. Hero Group Title
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    Are you in Calculus?

    • 2 years ago
  2. mskyeg Group Title
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    No im in Algebra 2

    • 2 years ago
  3. mskyeg Group Title
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    Hello?

    • 2 years ago
  4. mskyeg Group Title
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    @Hero left and i really need to get this done do you think you can help?

    • 2 years ago
  5. Mertsj Group Title
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    |dw:1352079518387:dw|

    • 2 years ago
  6. Mertsj Group Title
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    This function will have a maximum when h^2-18x + 80 is a maximum.

    • 2 years ago
  7. mskyeg Group Title
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    so how do i solve it?

    • 2 years ago
  8. freewilly922 Group Title
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    \[h^2 -18x +80\] is an open up parabola so doesn't have a max. Is this problem the type they will let you use graphing calculators on the assessment?

    • 2 years ago
  9. mskyeg Group Title
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    thankfully yes so do i just enter that equation into a calculator

    • 2 years ago
  10. Mertsj Group Title
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    But it does have a local maximum on the interval from 0 to 10

    • 2 years ago
  11. freewilly922 Group Title
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    If you can graph the function on the calculator there is usually a root finder or a point finder. Use this. @Mertsj, yes, but the local maximum of the function you gave \[h^2-18x +80\] will then be at 0 or 10 since it is an open up parabola. If you graph the cubic the local max they are looking for is between 0 and 8 since |dw:1352080536936:dw|

    • 2 years ago
  12. freewilly922 Group Title
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    Unless you meant the local min of the parabola?

    • 2 years ago
  13. mskyeg Group Title
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    These are the possibl answers how do i answer the question and find out which one it is 10 ft^3 107 ft^3 105 ft^3 110 ft^3

    • 2 years ago
  14. freewilly922 Group Title
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    Ok, if you can graph the function \[v(h) = h(h-8)(h-8)\] most calculators can find the points t they graphed, so you need to find the point that they ask for.... the maximum volume for the domain. Then ask yourself what is this. This is the height that gives you the maximum volume for that domain. You need the volume associated with it to choose an answer. They give you a function that gives you a volume when you plug into it a height. The trick is using your calculator to find the max.

    • 2 years ago
  15. mskyeg Group Title
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    I tried plugging it into the calculator and it says that its not valid

    • 2 years ago
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