Problem

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

Solution

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: \(\boxed{112.0}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7861/

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