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14 November, 11:30

Tanisha kicks a soccer ball during a game. The height of the ball, in feet, can be modeled by the function f (x) = - 16x squared + 48x, where x is the time in seconds after she kicks the ball. Graph the function. Find the maximum height of the ball and how long it takes the ball to reach that height?

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  1. 14 November, 11:34
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    The first thing we are going to do in this case is to rewrite the function:

    f (x) = - 16x ^ 2 + 48x

    We look for the first derivative:

    f ' (x) = - 32x + 48

    We match zero:

    0 = - 32x + 48

    We clear x:

    32x = 48

    x = 48/32 = 24/16 = 12/8 = 6/4 = 3/2

    x = 3/2

    We verify if this value is a maximum or minimum with the second derivative:

    f '' (x) = - 32

    We evaluate in x = 3/2:

    f '' (3/2) = - 32 (<0 Is a maximum)

    Therefore the maximum height is reached in:

    x = 1.5 s

    The height is:

    f (1.5) = - 16 * (1.5) ^ 2 + 48 * (1.5)

    f (1.5) = 36 feet

    Answer:

    The maximum height of the ball is:

    36 feet

    and it takes the ball to reach that height а bout:

    1.5 s
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