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 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.
is it c pls help me
at x = 4
h = -16 +32 + 2 = 18 ft
at x = 1
h = -1 +8 + 2 = 9 ft
so from x = 1 to x = 4, the water went up 9 feet
the average speed = 9/3 = 3 feet/second
so yes c
To find the average rate of change of a function, we need to calculate the difference in the function's values at the two given points and divide it by the difference in the x-values.
In this case, we are given f(x) = −x^2 + 8x + 2, and we need to find the average rate of change from x = 1 to x = 4.
Let's calculate the difference in the function's values at these two points:
f(4) = −(4)^2 + 8(4) + 2 = -16 + 32 + 2 = 18
f(1) = −(1)^2 + 8(1) + 2 = -1 + 8 + 2 = 9
Now, let's calculate the difference in the x-values:
Δx = 4 - 1 = 3
To find the average rate of change, we divide the difference in the function's values by the difference in the x-values:
Average Rate of Change = (f(4) - f(1)) / Δx
= (18 - 9) / 3
= 9 / 3
= 3
Therefore, the average rate of change of f(x) from x = 1 to x = 4 represents that the water rises up with an average speed of 3 feet per second during that time interval.
So, the correct answer is option C.