Posted by **ROBIN** on Friday, July 19, 2013 at 7:03pm.

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 -
**Graham**, Friday, July 19, 2013 at 7:19pm
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 -
**Steve**, Saturday, July 20, 2013 at 4:52am
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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