question given the function ( h(x) = x^2 - 6x + 4 ), determine the average rate of change of the function over the interval ( -2 leq x leq 5 ). answer attempt 1 out of 3 submit answer

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=-2 $ and $ b = 5 $.

## Step2: Calculate $ h(-2) $
Substitute $ x=-2 $ into $ h(x)=x^{2}-6x + 4 $:
$$
\begin{align*}
h(-2)&=(-2)^{2}-6(-2)+4\
&=4 + 12+4\
&=20
\end{align*}
$$

## Step3: Calculate $ h(5) $
Substitute $ x = 5 $ into $ h(x)=x^{2}-6x + 4 $:
$$
\begin{align*}
h(5)&=5^{2}-6(5)+4\
&=25-30 + 4\
&=-1
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{h(5)-h(-2)}{5-(-2)}$, substitute $ h(5)=-1 $ and $ h(-2)=20 $:
$$
\begin{align*}
\frac{h(5)-h(-2)}{5-(-2)}&=\frac{-1 - 20}{5 + 2}\
&=\frac{-21}{7}\
&=-3
\end{align*}
$$

# Answer:
$-3$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \( h(-2) \)

Step3: Calculate \( h(5) \)

Step4: Calculate the average rate of change

Answer: