Question

Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 6 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 of f(x) from x = 2 to x = 5 represent?

The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Answer 1

The answer to this question is:

D: The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Answer 2

F(x) = -x^2 + 6x + 6

where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds

rate of change of a distance is speed
at x=5, distance = 11
at x=2, distance = 14
so average rate of change = (14-11)/(5-2) = 1
so ans is D