Water coming out from a fountain is modeled by the function f(x) = -x^2 + 7x + 5 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 = 4 to x = 6 represent?

Question

Water coming out from a fountain is modeled by the function f(x) = -x^2 + 7x + 5 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 = 4 to x = 6 represent?

anonymous · Answer

The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.

 The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.

 The water travels an average distance of 5 feet from 4 seconds to 6 seconds.

 The water travels an average distance of 3 feet from 4 seconds to 6 seconds.

ranga · Answer

f(x) represents the height and x represents time.
Average rate of change of f(x) from x = 4 to x = 6 is:   { f(6) - f(4) } / (6 - 4) = 
 { f(6) - f(4) } / 2.   Calculate this.
Numerator is height (or distance) and the denominator is time.  Distance / time is speed.
With this information you can pick the correct answer.

anonymous · Answer

C or D?

ranga · Answer

Not allowed to give you the answer.  If you do the calculation in my first reply and know that distance / time is speed and not distance you will have the answer.