Question

find the average rate of change for the function between the given values. 17) f(x) = 4x^3 - 8x^2 - 1; from -4 to 1

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-4$, $b = 1$, and $f(x)=4x^{3}-8x^{2}-1$.

Step2: Calculate $f(a)$

First, find $f(-4)$:

$$
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$$

Step3: Calculate $f(b)$

Then, find $f(1)$:

$$
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$$

Step4: Calculate the average rate of change

Now, use the formula $\frac{f(b)-f(a)}{b - a}$:

$$
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$$

Answer:

76