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 \(\boxed{-4}\)