To find the average rate of change of the function on the interval [-1, 1], we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.
First, we find f(-1):
f(-1) = 2(-1)^2 + 2
f(-1) = 2(1) + 2
f(-1) = 2 + 2
f(-1) = 4
Next, we find f(1):
f(1) = 2(1)^2 + 2
f(1) = 2(1) + 2
f(1) = 2 + 2
f(1) = 4
Now, we calculate the difference in the function values and the difference in the x-values:
Δy = f(1) - f(-1) = 4 - 4 = 0
Δx = 1 - (-1) = 1 + 1 = 2
Finally, we calculate the average rate of change:
Average Rate of Change = Δy / Δx = 0 / 2 = 0
Therefore, the average rate of change of the function f(x) = 2x^2 + 2 on the interval [-1, 1] is 0.
etermine the average rate of change of the function on the given interval. Express your answer in exact simplest form.
f(x) = 2x^2+2
（b） on [-1,1］
1 answer