b) The average rate of change of the function $f(x)=7 x^{3}+7$ over the interval $[-4,4]$ is (Simplify your answer.)

Step 1 ：Given the function \(f(x) = 7x^3 + 7\) and the interval \([-4, 4]\).

Step 2 ：The average rate of change of a function over an interval \([a, b]\) is given by the formula: \[\frac{f(b) - f(a)}{b - a}\]

Step 3 ：Substitute the given values into the formula: \[\frac{f(4) - f(-4)}{4 - (-4)}\]

Step 4 ：Simplify the expression to get the average rate of change.

Step 5 ：The average rate of change of the function over the interval \([-4, 4]\) is 112.0.

Step 6 ：Final Answer: \(\boxed{112.0}\)