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Setting Up the Domain for Maxima/Minima Word Problems

  1. Mar 24, 2013 #1
    Good day everyone.
    I'm confused about how I SHOULD set up the domain of my function that models the word problem.

    Suppose I have a word problem that goes like this:
    A square box with no top is to be made by cutting congruent squares from the four corners of a square metal sheet and then folding up the resulting flaps. If the length of a side of the metal sheet is 12 in., how should the square be cut in order to make a box with the largest possible volume?

    Okay, so my volume equation is V(x)=(12-2x)(12-2x)(x)

    I know how to solve this kind of equation but, how do I know what interval I should consider?
    Should I use [0,6] or (0,6)?
    Can anyone give tips on how to know which one?
    My book used (0,6) but I don't really understand why. I know its meaningless to say you cut the corners by 0 cm^2, since you didn't really cut anything. Also 6cm^2, since by then none will be left for the open-top box. But how do I really know the domain of my function?

    I'm really confused. Help would be really appreciated.
  2. jcsd
  3. Mar 25, 2013 #2


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    Staff: Mentor

    [0,6] will work as well. You just get the issue that 0 and 6 might be local minima of the volume, and appear as option in the solution (as the derivative is zero there), even if you know already that they cannot be the solution.
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