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MATH

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Create a graph of a function given the following information:
The instantaneous rate of change at x = 2 is zero.
The instantaneous rate of change at x = 3 is negative.
The average rate of change on the interval 0 <x <4 is zero.

  • MATH -

    The instantaneous rate of change at x = 2 is zero.
    Means: A peak trough or inflection. The curve levels off there; the tangent is paralel to the x-axis.

    The instantaneous rate of change at x = 3 is negative.
    Means: There's a downward slop at x=3

    The average rate of change on the interval 0 <x <4 is zero.
    Means: It's symmetric over the interval - for every up there is a down, and you end as high as you start.

    Thus: It's a hill. Plot a parabola with a peak at x=2.

    Eg. Plot a curve between points:
    (0,0) (1,3) (2,4) (3,3) (4,0)

  • MATH -

    Good answer. They didn't actually ask for the function, so the above points (and also many other sets) will work.

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