Question

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.

Answer 1

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

Explanation:

I got it correct on the test

Answer 2

`f(x)=-x^(2) +8x+2`
Average rate of change from x = 1 to x = 4 =
`(f(4)-f(1))/(4-1)= (( -4^(2)+8(4)+2)-(- 1^(2)+8(1)+2))/(3)= ((-16+32+2)-(-1+8+2))/(3)= (18-9)/(3)=`
`(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