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Math Help - Need help with optimization(differentiation)

  1. #1
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    Exclamation Need help with optimization(differentiation)

    A rectangular piece of cardboard with dimension 12 cm by 24 cm is to be made into an open box (i.e., no lid) by cutting out squares from the corners and then turning up the sides. Find the size of the squares that should be cut out if the volume of the box is to be a maximum.
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  2. #2
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    Quote Originally Posted by ninja View Post
    A rectangular piece of cardboard with dimension 12 cm by 24 cm is to be made into an open box (i.e., no lid) by cutting out squares from the corners and then turning up the sides. Find the size of the squares that should be cut out if the volume of the box is to be a maximum.
    HI

    The volume would be ,

    V=(12-2x)(24-2x)(x)

    =288x-72x^2+4x^3

    \frac{dV}{dx}=288-144x+12x^2

    288-144x+12x^2=0

    Then here use the quadratic formula to solve for x .

    \frac{d^2V}{dx^2}=24x-144

    Substitute both values of x u got into this equation , whichever gives you <0 (since it is maximum) will be the answer .

    Then the size would be this x^2
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