Determine the average rate of change of the function on the given interval. Express your answer in exact simplest form.
f(x)=3 x^{2}+1
Answer
Final Answer: The average rate of change of the function on the interval [1, 2] is \(\boxed{9}\)
Step 1 ：Given the function \(f(x) = 3x^{2} + 1\)
Step 2 ：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 3 ：Let's assume the interval to be [1, 2] for this demonstration.
Step 4 ：Substitute a = 1 and b = 2 into the formula.
Step 5 ：Calculate \(f(b) - f(a)\) and \(b - a\) to get the average rate of change.
Step 6 ：The average rate of change of the function \(f(x) = 3x^{2} + 1\) on the interval [1, 2] is 9.0.
Step 7 ：Final Answer: The average rate of change of the function on the interval [1, 2] is \(\boxed{9}\)
