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Math Help - Finding a maximum X value for equation.

  1. #1
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    Finding a maximum X value for equation.

    Im having a hard time finding a maximum value. Well, i can find it, but its not the correct value.

    Here is the problem:

    A rectangular piece of cardboard measuring 26 inches by 47 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let X represent the length of each side of each such square. For what value of X will the volume be a maximum ?


    So Im thinking the equation is set up like this:

    (26-2x)(47-2x)(x)=V

    And after foiled out:

    x(4x^2-146x+1222)

    and then I apply vertex formula to get the x value: -b/2a= 146/8= 18.25

    Wouldnt 18.25 be the x value? Its says the correct answer is 5.37. What am I doing wrong?
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  2. #2
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    Quote Originally Posted by Jerry99 View Post
    Im having a hard time finding a maximum value. Well, i can find it, but its not the correct value.

    Here is the problem:

    A rectangular piece of cardboard measuring 26 inches by 47 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let X represent the length of each side of each such square. For what value of X will the volume be a maximum ?


    So Im thinking the equation is set up like this:

    (26-2x)(47-2x)(x)=V

    And after foiled out:

    x(4x^2-146x+1222)

    and then I apply vertex formula to get the x value: -b/2a= 146/8= 18.25

    Wouldnt 18.25 be the x value? Its says the correct answer is 5.37. What am I doing wrong?
    Dear Jerry99,

    I noticed that this is in the pre-calculus sub forum. The equation you have is a cubic not a quadratic and will need Calculus (the derivative ) to find its max volume. You could also graph the cubic and find is maximum value that way but it would only be an estimate.
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  3. #3
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    Im having a hard time finding an appropriate viewing window on my calculator to see this functions maximum. Any suggestions?
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Jerry99 View Post
    Im having a hard time finding an appropriate viewing window on my calculator to see this functions maximum. Any suggestions?
    x should go from 0 to 13 and y should go from 0 to 3000. you may want to scale your y axis in 500 or so as well.
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  5. #5
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    thanks for the help
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