The area of a rectangle can be modeled by A = b (4-b ), where A is the area of the rectangle, and b is the length of the base (in inches). ?

What is the greatest possible area of the rectangle?

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  • 1 month ago

    A = b ( 4 - b )  =  4 b - b²

    dA/db  =  4 - 2 b

    For maximum Area, dA/db  =  0

    => 4 - 2 b  =  0

    => b  =  2

    Then A will be equal to --

    A  =  2 ( 4 - 2 )  =  4 sqr inch ................. Answer

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  • 1 month ago

    A = b (4 - b)

    A = 4b - b² 

    This is a parabola 

    -b² + 4b - A = 0

    Since the coefficient of b² is negative the parabola opens down

    and the vertex is a maximum

    The roots are

    b = 0

    (4 - b) = 0 ===> b = 4

    b = {0, 4}

    -------------------------

    the vertex occurs at the midpoint of the roots

    b = (0 + 4) / 2

    b = 2

    The maximum will be

    A = 2(4 - 2)

    A = 2 * 2

    A = 4 in² <–––––

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