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.

Question

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

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

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

C.The water rises up an average distance of 3 feet from 1 second to 4 seconds.

D.The water rises up an average distance of 2 feet from 1 second to 4 seconds.

I think the answer is A.

Answer 1

f(1) = -1 + 8 + 2 = 9
f(4) = -16 + 32 + 2 = 18

avg rate of change = (18-9)/(4-1) = 3 ft/s

this is a rate, you matches it up with A, which states a distance.
You need a rate or speed, so it must be C