Water coming out from a fountain is modeled by the function f(x) = −x2 + 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 of f(x) from x = 1 to x = 4 represent, options AWhat does the average rate of change of f(x) from x = 1 to x = 4 represent?
options: 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.
\(f(x)=-x^{2} +8x+2\) Average rate of change from x = 1 to x = 4 = \(\frac{f(4)-f(1)}{4-1}= \frac{( -4^{2}+8(4)+2)-(- 1^{2}+8(1)+2)}{3}= \frac{(-16+32+2)-(-1+8+2)}{3}= \frac{18-9}{3}=\)\(\frac{9}{3}=3\)
This means that the water rises up with an average speed of 3 feet per second from 1 second to 4 seconds
