find the average rate of change of the function $f(x) = -1x^2 - 6x - 8$, on the interval $2,3$.

average rate of change =
give exact answer!

Question

find the average rate of change of the function $f(x) = -1x^2 - 6x - 8$, on the interval $2,3$.

average rate of change =
give exact answer!

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $ f(x) $ on the interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. Here, $ a = 2 $, $ b = 3 $, and $ f(x)=-x^{2}-6x - 8 $.

## Step2: Calculate $ f(3) $
Substitute $ x = 3 $ into $ f(x) $:
$$
\begin{align*}
f(3)&=- (3)^{2}-6(3)-8\
&=-9 - 18 - 8\
&=-35
\end{align*}
$$

## Step3: Calculate $ f(2) $
Substitute $ x = 2 $ into $ f(x) $:
$$
\begin{align*}
f(2)&=- (2)^{2}-6(2)-8\
&=-4 - 12 - 8\
&=-24
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{f(b)-f(a)}{b - a}$ with $ a = 2 $, $ b = 3 $, $ f(3)=-35 $, and $ f(2)=-24 $:
$$
\begin{align*}
\frac{f(3)-f(2)}{3 - 2}&=\frac{-35-(-24)}{1}\
&=\frac{-35 + 24}{1}\
&=-11
\end{align*}
$$

# Answer:
$-11$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \( f(3) \)

Step3: Calculate \( f(2) \)

Step4: Calculate the average rate of change

Answer: