Determine the average rate of change of the function on the given interval. Express your answer in exact simplest form.
\[
f(x)=2 x^{2}+2
\]

Part 1 of 3
(a) on $[-2,0]$

The average rate of change of the function is $\square$.

Part 2 of 3
(b) on $[3,4]$

The average rate of change of the function is $\square$.
Check
Q 2023 McGraw Hill LLC. All Rights

Step 1 ：The average rate of change of a function on an interval [a, b] is given by the formula: \(\frac{f(b) - f(a)}{b - a}\)

Step 2 ：To find the average rate of change of the function \(f(x) = 2x^2 + 2\) on the intervals [-2, 0] and [3, 4], we need to substitute the values of a and b into the formula and simplify.

Step 3 ：Let's start with the interval [-2, 0]. Here, a = -2 and b = 0.

Step 4 ：Substitute a = -2 and b = 0 into the formula, we get \(\frac{f(0) - f(-2)}{0 - (-2)}\)

Step 5 ：Simplify the above expression, we get -4.0

Step 6 ：The average rate of change of the function \(f(x) = 2x^2 + 2\) on the interval [-2, 0] is -4.

Step 7 ：Final Answer: The average rate of change of the function on the interval [-2, 0] is \(\boxed{-4}\)