Math

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Gina has 24 feet of fence, she wants to make the largest rectangular area possible for her rabbit to play in , what length should she make each side of the rabbit penn?

  • Math -

    That is calculus question.


    a = length

    b = width

    P = Perimeter

    A = Area



    P = 2 a + 2 b = 2 ( a + b )

    24 = 2 ( a + b ) Divide both sides by 2

    12 = a + b

    a + b = 12 Subtract a to both sides

    a + b - a = 12 - a

    b = 12 - a


    A = a * b = a * ( 12 - a )

    A = 12 a - a ^ 2


    The function has a minimum value if f ' ( A ) = 0

    and f " ( A ) = a positive number.


    The function has a maximum value if f '( A ) = 0

    and f ''( A ) = a negative number.


    f ´ ( A ) = 12 - 2 a

    f " ( A ) = - 2



    f´ ( A ) = 0

    12 - 2 a = 0 Add 2 a to both sides

    12 - 2 a + 2 a = 0 + 2 a

    12 = 2 a Divide both sides by 2

    6 = a

    a = 6 m


    f´ ( A ) = 0

    f " ( A ) = - 2

    That is a maximum value.


    b = 12 - a = 12 - 6 = 6 m


    Square 6 x 6 m

  • Math -

    How do I figure out the largest rectangle area

  • Math -

    you solve it

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