What is the average rate of change of the function below on the interval [-4,-3]?
f(x)=- 1/x^3
No help
that would be
(f(-3)/(f(-4))/(-3-(-4))
= (1/27 - 1/64)/1 = 37/1728
To find the average rate of change of a function on a given interval, you need to evaluate the function at the endpoints of the interval and then calculate the difference in the function values divided by the difference in the input values.
In this case, we are asked to find the average rate of change of the function f(x) = -1/x^3 on the interval [-4, -3].
First, let's calculate the function values at the endpoints of the interval.
At x = -4:
f(-4) = -1/(-4)^3 = -1/(-64) = -1/(-64) = 1/64
At x = -3:
f(-3) = -1/(-3)^3 = -1/(-27) = -1/(-27) = 1/27
Now, we calculate the difference in the function values:
Δf = f(-3) - f(-4) = (1/27) - (1/64)
Next, we calculate the difference in the input values:
Δx = -3 - (-4) = -3 + 4 = 1
Finally, we find the average rate of change:
Average Rate of Change = Δf / Δx = [(1/27) - (1/64)] / 1 = (64-27)/(27*64) = (37)/(27*64) ≈ 0.0220
Therefore, the average rate of change of the function f(x) = -1/x^3 on the interval [-4, -3] is approximately 0.0220.