Water coming out from a fountain is modeled by the function f (x) = - x^2+8x+2 where f (x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change f (x) from x=1 to x=4 represent?

The water travels an average distance of 3 feet from 1 second to 4 seconds.

The water travels an average distance of 2 feet from 1 second to 4 seconds.

The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.

The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.

Question

Mathematics

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13 January, 02:00

Water coming out from a fountain is modeled by the function f (x) = - x^2+8x+2 where f (x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change f (x) from x=1 to x=4 represent?

The water travels an average distance of 3 feet from 1 second to 4 seconds.

The water travels an average distance of 2 feet from 1 second to 4 seconds.

The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.

The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.

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Uriah · Answer 1

The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds. The vertical increase from x = 1 to x = 4, on the y (i. e. f (x)) - axis, represents an increase in the height of the water, since f (x) represents the height, in feet, of the water from the fountain at different times. Graph included below.