Final answer:
The average rate of change of the function f(x) = -x^4 + 4x over the interval [-2, 5] is calculated using the formula for average rate of change and is approximately -83.00.
Step-by-step explanation:
To find the average rate of change of the function f(x) = -x^4 + 4x over the interval [-2, 5], we use the formula for the average rate of change which is (f(xf) - f(xo))/(xf - xo), where xf is the final value and xo is the initial value in the interval. First, we calculate the function values at the endpoints of the interval: f(-2) and f(5).
f(-2) = -(-2)^4 + 4(-2) = -16 - 8 = -24
f(5) = -(5)^4 + 4(5) = -625 + 20 = -605
Now, we plug these values into the formula for the average rate of change:
Average rate of change = (f(5) - f(-2))/(5 - (-2)) = (-605 - (-24))/(5 - (-2)) = (-605 + 24)/7 = -581/7 ≈ -83.00
Therefore, the average rate of change of the function on the interval [-2, 5] is approximately -83.00.