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?

The average rate of change of f(x) form x =1 to x=4 is 3 and it represent that on average every unit of time between 1 and 4, the height of the fountain change 3 feets.

Step-by-step explanation:

the function f(x) represent the height of the water from the fountain at different times. With this equation we can calculate the difference height at time x=1 and a time x=4.

1. For x=1

Replacing x by 1 on the function f(x)=-x^2+8x+2:

f(1) = -(1)^2 + 8(1) + 2

f(1) = -1 + 8 + 2 = 9

The height of the water at 1 unit of time is 9 feets.

2. For x=4

Replacing x by 1 on the function f(x)=-x^2+8x+2:

f(4) = -(4)^2 + 8(4) + 2

f(1) = -16 + 32 + 2 = 18

The height of the water at 4 unit of time is 18 feets.

In general, the average rate of change f(x) from x=a to x=b is expressed by:

So, the average rate of change of f(x) from x=1 to x=4 is calculate as:

=

= 3 feets /unit of time

Taking into account the units obtain from the equation above, the average rate of change is saying that between 1 to 4 units of time, every unit of time the height of the water changed 3 feets.

answer: the answer is 127 degrees

the answer is 1/4

step-by-step explanation: