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Math Help - Find the Max Volume of a box using Calc

  1. #1
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    Find the Max Volume of a box using Calc

    Find the max volume of a box with a square base if you have 1200 sq. ft. of material for sides and a bottom (assuming open top).

    I'm screwing up somewhere but I can't figure out where. V= x^2*y and then your y= (1200-x^2)/4x

    Using a graphical method I found the answer x to be 20. But how do you get here using calculus?
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  2. #2
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    V=x^2y=x^2(\frac{1200-x^2}{4x}=\frac{1200x-x^3}{4}

    Find where:
    V'(x)=0
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  3. #3
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    Okay, I see that you substituted the y equation immediately into the volume equation.

    Why couldn't you take the derivative of x^2*y to get:

    vol'(x)= x^2((1200-x^2)(4) - 4x(-2x))/(4x)^2 + 2xy

    as in lets v=X^2 and let u=y

    then vol'(x)= v*u' + u*v'

    When I work this out I get x=60 and y= -10 which is obviously NOT the answer
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  4. #4
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    Quote Originally Posted by MrJoe2000 View Post
    Okay, I see that you substituted the y equation immediately into the volume equation.

    Why couldn't you take the derivative of x^2*y to get:

    vol'(x)= x^2((1200-x^2)(4) - 4x(-2x))/(4x)^2 + 2xy
    You are differentiating y wrong, using the quotient rule backwards:
    dy/dx= (-2x(4x)- 2x(1200- x^2)/(4x)^2

    as in lets v=X^2 and let u=y

    then vol'(x)= v*u' + u*v'

    When I work this out I get x=60 and y= -10 which is obviously NOT the answer
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  5. #5
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    Why do I take the quotient rule backwards?
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