question
given the function ( h(x) = -x^2 - 10x + 29 ), determine the average rate of change of the function over the interval ( -6 leq x leq -1 ).
answer
attempt 1 out of 3
submit answer
watch video
show examples

Question

Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $ h(x) $ over the interval $[a, b]$ is given by $\frac{h(b)-h(a)}{b - a}$. Here, $ a=-6 $ and $ b = - 1$.

## Step2: Calculate $ h(-6) $
Substitute $ x=-6 $ into $ h(x)=-x^{2}-10x + 29 $:
$$
\begin{align*}
h(-6)&=-(-6)^{2}-10\times(-6)+29\
&=-36 + 60+29\
&=24 + 29\
&=53
\end{align*}
$$

## Step3: Calculate $ h(-1) $
Substitute $ x = - 1$ into $ h(x)=-x^{2}-10x + 29 $:
$$
\begin{align*}
h(-1)&=-(-1)^{2}-10\times(-1)+29\
&=-1 + 10+29\
&=9 + 29\
&=38
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{h(b)-h(a)}{b - a}$ with $ a=-6 $, $ b=-1 $, $ h(-6) = 53$ and $ h(-1)=38$:
$$
\begin{align*}
\frac{h(-1)-h(-6)}{-1-(-6)}&=\frac{38 - 53}{-1 + 6}\
&=\frac{-15}{5}\
&=- 3
\end{align*}
$$

# Answer:
$-3$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \( h(-6) \)

Step3: Calculate \( h(-1) \)

Step4: Calculate the average rate of change

Answer: